Pay Factors for Asphalt-Concrete Construction: Effect of … · Technical Memorandum TM-UCB-PRC-2001-1 Pay Factors for Asphalt-Concrete Construction: Effect of Construction Quality

Technical Memorandum

TM-UCB-PRC-2001-1

Pay Factors for Asphalt-Concrete Construction:

Effect of Construction Quality on Agency Costs

Prepared for

California Department of Transportation

by

John A. Deacon, Carl L. Monismith, John T. Harvey, and Lorina Popescu

February 2001

Pavement Research CenterInstitute of Transportation StudiesUniversity of California, Berkeley

iii

TABLE OF CONTENTS

Table of Contents ...........................................................................................................................iii

List of Tables................................................................................................................................... v

List of Figures ................................................................................................................................xi

1.0 Introduction ............................................................................................................................. 1

2.0 Concept.................................................................................................................................... 2

3.0 Models..................................................................................................................................... 3

3.1 Performance Models ........................................................................................................... 4

3.1.1 Variability Considerations........................................................................................... 4

3.1.2 Fatigue Cracking ......................................................................................................... 5

3.1.3 Permanent Deformation ............................................................................................ 17

3.2 Cost Model ........................................................................................................................ 28

4.0 Pay Factors ............................................................................................................................ 31

4.1 Pay Factors—Twenty-Year Expected Pavement Life ...................................................... 33

4.2 Pay Factors—Influence of Expected Pavement Life and Cost Parameters ...................... 48

4.3 Comparison of Current Caltrans Pay Factors with Those Obtained from Performance

Models Presented Herein .......................................................................................................... 49

4.4 Combined Pay Factors ...................................................................................................... 62

5.0 Discussion ............................................................................................................................. 65

6.0 References ............................................................................................................................. 67

Appendix A: RELIABILITY AND VARIABILITY CONSIDERATIONS ................................ 69

Reliability.................................................................................................................................. 69

Variability.................................................................................................................................. 70

Appendix B ................................................................................................................................... 78

iv

Appendix C: Analytically-Based Approach to Rutting Prediction ............................................... 79

Mechanistic-Empirical Approach ............................................................................................. 79

v

LIST OF TABLES

Table 3.1 Construction Variation of Mix and Structural Characteristics 7

Table 3.2 Materials/Construction Component of Total Construction Variance...............................7

Table 3.3 Variation of Mix and Structural Characteristics for Monte Carlo Simulations 7

Table 3.4 Construction Targets 10

Table 3.5 Levels and Ranges for Variable Evaluated 10

Table 3.6 Summary of Parameters in Example 14

Table 3.7 Regression Coefficients Relating ln(ESALs) to Mix Variables for Specific

Levels of Rutting 17

Table 4.1 Effect of off-target asphalt content on future agency resurfacing cost based on

rutting in WesTrack pavements (change expressed as a percent of new pavement

construction cost). 34

Table 4.2 Effect of off-target air-void content on future agency resurfacing cost based on

rutting in WesTrack pavement (change expressed as a percent of new pavement


Table 4.3 Effect of off-target mineral filler on future agency resurfacing cost based on



Table 4.4 Effect of off-target fine aggregate on future agency resurfacing cost based on



Table 4.5 Effect of off-target asphalt content on future agency rehabilitation cost based

on Caltrans fatigue model (change expressed as a percent of new pavement


vi

Table 4.6 Effect of off-target air-void content on future agency rehabilitation cost based


construction cost). ................................................................................................................. 39

Table 4.7 Effect of off-target asphalt-concrete thickness on future agency rehabilitation

cost based on Caltrans fatigue model (change expressed as a percent of new

pavement construction cost).................................................................................................. 40

Table 4.8 Effect of off-target asphalt content on future agency resurfacing/rehabilitation

costs (change expressed as a percent of new pavement construction cost). ......................... 41

Table 4.9 Effect of off-target air-void content on future agency resurfacing/rehabilitation


Table 4.10 Effect of off-target mineral filler on future agency resurfacing/rehabilitation


Table 4.11 Effect of off-target fine aggregate on future agency resurfacing/rehabilitation


Table 4.12 Effect of off-target asphalt concrete thickness on future agency

resurfacing/rehabilitation costs (change expressed as a percent of new pavement

construction cost). ................................................................................................................. 45

Table 4.13 Contractor pay factors for asphalt content (percentage of future

resurfacing/rehabilitation cost in current-year dollars). ........................................................ 46

Table 4.14 Contractor pay factors for air-void content (percentage of future


Table 4.15 Contractor pay factors for asphalt-concrete thickness (percentage of future


vii

Table 4.16 Contractor pay factors for mineral filler (percentage of future


Table 4.17 Contractor pay factors for fine aggregate (percentage of future


Table 4.18 Effect of off-target asphalt content on future agency resurfacing cost based

on rutting in WesTrack pavements (change expressed as a percent of new pavement

construction cost); target life = 10 years, r = 3.5 percent...................................................... 50

Table 4.19 Effect of off-target asphalt content on future agency rehabilitation cost based



Table 4.20 Effect of off-target asphalt content on future agency

resurfacing/rehabilitation costs (change expressed as a percent of new pavement



resurfacing/rehabilitation cost in current-year dollars); target life = 10 years, r = 3.5

percent. .................................................................................................................................. 53



percent. .................................................................................................................................. 53



percent. .................................................................................................................................. 54

viii



percent. .................................................................................................................................. 54



percent. .................................................................................................................................. 55



percent. .................................................................................................................................. 55



percent. .................................................................................................................................. 56



percent. .................................................................................................................................. 56



percent. .................................................................................................................................. 57



percent. .................................................................................................................................. 57

ix



percent. .................................................................................................................................. 58



percent. .................................................................................................................................. 58



percent. .................................................................................................................................. 59


resurfacing/rehabilitation cost in current-year dollars) ; target life = 20 years, r = 3.5

percent. .................................................................................................................................. 59



percent. .................................................................................................................................. 60

Table 4.36 Pay Factor Summary—Overlay Project, SR 299, Trinity County, July 1999 .......... 60

Table 4.37 Pay Factors for Combination Conditions (from Simulations) (Conditions Set

to Yield Individual Pay Factors of About –20 Percent) ........................................................ 64

Table 4.38 Pay Factors for Combination Conditions (from Simulations) (Conditions Set

to Yield Varying Individual Pay Factors) ............................................................................. 64

Table 4.39 Pay Factors for Combination Conditions (from Calculations) (Conditions Set

to Yield Varying Individual Pay Factors) ............................................................................. 64

Table B-1 Pavement Structures.................................................................................................. 78

x

Table C-1 Calculated ESALs to a range in rut depths for a constant loading of 60

trucks/hour, WesTrack environment. .................................................................................... 86

Table C-2 Calibration of equations for simulating ln(field a) based on mix and RSST

variables. ............................................................................................................................... 91

Table C-3 Calibration of equations for simulating field c based on mix and RSST

variables. ............................................................................................................................... 93

xi

LIST OF FIGURES

Figure 3.1 Outlines of performance model simulations for fatigue cracking and rutting. 6

Figure 3.2. Effects of as-constructed air-void content on pavement fatigue performance. 12

Figure 3.3. Effects if as-constructed asphalt content on pavement fatigue performance. 12

Figure 3.4. Effects of as-constructed surface thickness on pavement fatigue performance. 13

Figure 3.5. Effect of specification failure level on acceptability of mix compaction. 13

Figure 3.6. Influence of air-void content on pavement performance. 14

Figure 3.7. Expected pavement performance. 15

Figure 3.8. Influence of air-void content on contractor pay adjustment. 16

Figure 3.9. Influence of pavement performance on pay factors. 16

Figure 3.10. WesTrack gradings. 19

Figure 3.11. Effect of mix variables on simulated ESALs to 15 mm (0.6 in.) rut depth for

a range in fine aggregate contents; Vair = 6.5%, P200 = 6.0%. 20

Figure 3.12 Effect of mix variables on simulated ESALs to 15 mm (0.6 in.) rut depth for

a range in P200; Vair = 6.5%, fine aggregate = 28%. 21


a range in air-void contents; P200 = 6.0%, fine aggregate = 28%. 22


a range in asphalt contents; P200 = 6.0%, fine aggregate = 28%. 23

Figure 3.15. Influence of as-constructed asphalt contetn on rutting performance. 24

Figure 3.16. Influence of as-constructed air-void content on rutting performance. 25

Figure 3.17. Influence of as-constructed asphalt content on pavement rutting performance. 26

Figure 3.18. Influence of as-constructed asphalt content on pavement rutting

performance. 27

xii

Figure 3.19. Schematic illustration of annual costs of on-target and off-target

construction. 30

Figure A-1. Major components of testing and construction variance. 77

Figure C-1. WesTrack pavement respresentation for mechanistic-empirical modeling for

rutting. 81

Figure C-2. Time-hardening provedure for plastic strain accumulation under stress

repetitions of different magnitudes in compound loading. 83

Figure C-3. Framework for rut depth estimates. 85

Figure C-4. Comparison between computed and measured rut depth versus time;

Section 4. 87


Section 7. 88


Section 19. 89


Section 38. 90

Figure C-8. Permanent shear strain, iγ , versus load repetitions, n; rsst = 3778. 92

1

1.0 INTRODUCTION

The quality of the construction process is a major factor in determining how well a

pavement will perform under traffic loading and when subjected to environmental influences.

To improve the construction process, quality control/quality assurance (QC/QA) procedures and

pay incentives have been instituted in recent years. It is the objective of this report to

demonstrate a rational and feasible method for quantitatively establishing penalties/bonuses for

asphalt concrete construction with the initial emphasis placed on new asphalt concrete pavement

construction.

The approach makes use of performance models for asphalt concrete used to interpret the

results of the CAL/APT program (1) and WesTrack (2). The performance model for fatigue

resulted from the CAL/APT program while the one for rutting came from the WesTrack

accelerated pavement test program. For both modes of distress the system considers the means

and variances of asphalt content, air-void content, asphalt-concrete thickness, and aggregate

gradation. In estimating damage under traffic loading, the pavement is treated as a multilayer,

elastic system. The performance models compute the distribution of pavement life, expressed as

ESALs, using Monte Carlo simulation techniques.

Costs are established using a cost model which considers only the time to the next

rehabilitation activity. It understates agency costs by ignoring possible effects of construction

quality on future rehabilitation costs: it ignores future rehabilitation activity beyond the first

cycle. It requires an exogenous estimate of future rehabilitation costs, traffic growth, expected

years of new-pavement life, and a discount rate representing the time value of money.

The development of single sets of pay factors including both fatigue and rutting reflects

the following. The recommended bonus for superior work is the smaller of that for either fatigue

or rutting. For asphalt content, there are no bonuses for “dry” mixes. While such mixes may be

2

rut resistant, they may lead to early fatigue distress. The penalty for larger-than-target asphalt

content is determined by reduction in rutting resistance caused by surplus asphalt. For asphalt-

concrete thickness, the recommended pay factors are based only on fatigue performance while

for aggregate gradation, the recommended pay factors are based primarily on rutting. For air-

void content, the recommended pay factors reflect both fatigue and rutting considerations.

2.0 CONCEPT

Contractor pay incentives serve at least two objectives: (1) they encourage the contractor

to construct pavements with significantly improved performance in comparison to those meeting

minimum specification requirements, while at the same time, maintaining costs at reasonable

levels; and (2) they provide a rational alternative for dealing with marginally

inadequate/adequate construction. Many factors must be considered in the establishment of pay

schedules that not only realize these objectives but are mutually agreeable to the highway agency

and the contractor.

The approach taken herein for the development of pay factors focuses primarily on the

economic impacts to the highway agency. In this approach, the assumption is that an appropriate

penalty for inferior construction should be the added cost to the agency and that the bonus for

superior construction should be no greater than the added savings to the agency.

For new construction, for example, these agency costs/savings are associated primarily

with subsequent pavement rehabilitation. Inferior construction hastens the need for future

rehabilitation and may increase the cost of rehabilitation as well. As a result, inferior

construction increases the present worth of future rehabilitation costs. Superior construction, on

the other hand, reduces the present worth of these costs, largely by deferring the future

rehabilitation. The difference in present worths of rehabilitation costs, as constructed versus as

3

specified and as expected, provides a rational basis for setting the level of penalty/bonus for

inferior/superior construction quality.

3.0 MODELS

To compute the differential present worth of future rehabilitation requires two different

types of models: (1) a performance model or models for determining the effect of construction

quality on expected pavement performance; and (2) a cost model for translating these effects into

rehabilitation dollars.

Two performance models are described herein: one for fatigue cracking and the other for

rutting. For most construction situations, both performance models must be utilized to develop

appropriate pay factors. For this situation, the pay factors resulting from the use of the

performance models are based on the distress mode yielding the most beneficial consequence to

the agency; namely, smaller bonus and larger penalty. There may be circumstances in which

either of the two distress modes will be applicable. These situations will not be discussed herein

although the necessary information to do so is included.

The performance model used for fatigue is based on the mix analysis and design system

originally developed as a part of SHRP (3), extended to efficiently treat in-situ temperatures (4),

calibrated to the current Caltrans flexible pavement design system (5), extended to incorporate

construction variability (6), and used in interpreting the results of HVS tests on flexible

pavements, both new and overlaid, constructed at the Richmond Field Station according to

Caltrans Standards (1). The model used for rutting is based on mix performance data developed

at WesTrack (2).

In estimating damaging strains under traffic for fatigue cracking, the pavement is treated

as a multilayer elastic system. For rutting, the performance model is based on regression

4

analysis although multilayer elastic analysis was used in its development as well. In both

models, Monte Carlo simulations are used to obtain distributions of pavement lives.

The cost model considers only the time to the next rehabilitation activity; i.e., it ignores

future rehabilitation measures beyond the first cycle. It requires an estimate of future

rehabilitation cost; it considers annual inflation of rehabilitation costs, traffic growth, expected

years of the constructed life of the asphalt concrete, and a discount rate representing the time

value of money.

3.1 Performance Models

The processes embedded within the performance models are illustrated schematically in

Figure 3.1. Figure 3.1a shows the process for fatigue cracking and Figure 3.1b is that for rutting.

Central to these processes is the random selection of construction variable including air-void

content, asphalt content, aggregate gradation, and asphalt concrete thickness.1 For rutting, the

variables considered are air-void content, Vair, asphalt content, PWasp, and aggregate gradation

expressed in terms of the percent passing the No. 200 (0.075 mm) sieve, P200, and the fraction

passing the No. 8 (2.38 mm) sieve and retained on the No. 200 (0.075 mm) sieve, fa. For

fatigue, the variables include air-void content, asphalt content, and asphalt concrete thickness, t.

3.1.1 Variability Considerations

To consider the variability referred to in Figures 3.1a and 3.1b, the random selection of

the variables assumes normally distributed random variables with known or assumed means and

1 While not shown in Figure 3.1a (fatigue cracking) because it is only incidental to the computations, a randomselection was also made of the foundation modulus, a modulus representing the composite effects of base, subbase,and subgrade layers in an “equivalent” two-layer system.

5

variances. Of particular significance are the variances that might be expected under normal

construction operations. Estimates of these variances were obtained from a combination of

literature evaluation, back calculation of moduli from Falling Weight Deflectometer (FWD)

measurements, and data collected as a part of the WesTrack project (7). A summary of these

results are presented in Table 3.1.

The totals in Table 3.1 include not only materials and construction components, but also

components resulting from testing and sampling. To consider only materials and construction

effects, the testing and sampling components were removed from the variance estimates using

information contained in Table 3.2. Table 3.3 summarizes the results of this analysis, which is

briefly described in Appendix A (6). The equations for estimating the standard deviation of

asphalt-concrete thickness were developed as an approximate way to handle multilift

construction. Among the assumptions made in their development was that the coefficient of

variation of thickness in single-lift construction is about 14 percent.

3.1.2 Fatigue Cracking

The performance model used for fatigue follows the procedure illustrated schematically

in Figure 3.1a. It is based on the procedure described in Reference (5) utilizing fatigue test data

representative of mixes containing dense-graded aggregates meeting State of California

specifications.2

2 These gradings generally lie closer to the 0.45 curve than either the fine or coarse gradings used at WesTrack;however, the fatigue response of these mixes is likely similar to that of the mixes with the fine grading used atWesTrack.

6

Begin

Random selection of air-void content

Random selection of asphalt content

Random selection of asphalt-concrete thickness

Calculation of asphalt-concrete stiffness

Calculation of flexural strain in asphalt concrete

Calculation of "laboratory"fatigue life

Application of shift factor andtemperature conversion factor

Update of frequency distributionof "in-situ" fatigue life

More iterations?

End

No

Yes

3.1a

Begin

Determination of ESALs15*

Regression of ESALs15 withasphalt content, air-void content,

and gradation

Random selection of air-voidcontent

Random selection of asphaltcontent

Random selection of gradation(P200, fa)

Update of frequency distributionof "in-situ" rutting life

More iterations?

End

No

Yes

3.1b

Figure 3.1 Outlines of performance model simulations for fatigue cracking and rutting.

7

Table 3.1 Construction Variation of Mix and Structural Characteristics

Property Measure of Variation Value orRange Source

AsphaltContent

Standard DeviationStandard DeviationStandard DeviationStandard Deviation

0.15–0.44%0.1–0.4%

0.31%0.3%

Table 12.46 (7)Individual WesTrack sections (7)

WesTrack composite (7)Table 3 (8)

Air-voidContent

Standard DeviationStandard DeviationStandard DeviationStandard Deviation

0.9–1.9%0.4–1.5%

1.5%1.94%



Thickness

Coefficient of VariationStandard DeviationStandard DeviationStandard Deviation

12.5–15%0–0.5 cm0.58 cm0.99 cm



FoundationModulus

Coefficient of VariationCoefficient of VariationCoefficient of VariationCoefficient of Variation

11.3–14.7%17.3–44.7%3.6–17.7%14.2–28.5%

HVS test sections at UCB (1)Segment of highway in KY*

Individual WesTrack sections (7)WesTrack composite (7)

* Unpublished data, Kentucky DOT

Table 3.2 Materials/Construction Component of Total Construction Variance

Property Materials/ConstructionComponent (%) Source

Asphalt Content 4061

Figure 7 (9)Table 3 (8)

Air-Void Content 6090

Table 8 (inferred) (9)Table 3 (8)

Thickness 95 Table 3 (8)Foundation Modulus 70 Assumed

Table 3.3 Variation of Mix and Structural Characteristics for Monte CarloSimulations

Property Total StandardDeviation

Percentage of VarianceDue to

Materials/Construction

Materials/ConstructionComponent of Standard

DeviationAsphalt Content 0.30% 40 0.19%

Air-Void Content 1.6% 60 1.2%Asphalt Concrete

Thickness, t ( )cmt 69.0200.0 ⋅ 80 ( )cmt 69.0173.0 ⋅

FoundationModulus

30% (coefficientof variation) 70 25%

8

Multilayer elastic analysis with ELSYM5 was used to simulate the stress and strain states

with structures designed according to the State of California procedures. Table B-1 in Appendix

B provides a summary of the pavement structures analyzed. Loading consisted of a dual-tire

assembly of 9000 lbs. (40 kN) with a center-to-center spacing of 12 in. (300 mm) and a tire

contact pressure of 100 psi (690 kPa). The critically stressed location for fatigue was assumed to

be at the bottom boundary of the asphalt concrete layer.

As noted above, mix properties for use in the analysis were obtained by testing a

representative mix, the constituents for which included an AR-4000 asphalt cement from a

source in the Central Valley and a granite from the Logan quarry in Watsonville. The aggregate

gradation passed between the middle limits of the Caltrans 3/4 in. medium and coarse gradations.

Stiffness, Smix, and fatigue life, Nf, calibrations for this mix at 20°C (68°F) are as follows

(5):

( )Waspairmix PVS 17233.07577.0259.15exp −−= (3.1)

( )tWaspairf PVN εln71763.3575199.0164566.00012.22exp −+−−= (3.2)

Each of the Monte Carlo simulations produced an independent estimate of the laboratory

fatigue life, Nf . The corresponding simulated in-situ life, ESALs, was computed by applying a

shift factor, SF, and a temperature conversion factor, TCF, as follows:

TCFSFN

ESALs f ⋅= (3.3)

The shift factor is an empirically derived factor that accounts for differences between the

laboratory and the in-situ pavement in the rate at which fatigue damage accumulates with each

load application. For computations reported herein, the shift factor was calibrated to the Caltrans

design model following procedures described in Reference (5). Thickness replaced strain as the

9

independent variable, however, and engineering judgement was used to develop reasonable

estimates for the thickest and thinnest pavement sections. The shift factor was computed as

follows:

( ) 12t fortSF >−+= 1244.648.30 (3.4)

12t for3.6ttSF ≤≤+−= 5121.76109.23771.0 2 (3.5)

and

6.33 <= t forSF (3.6)

in which t is the asphalt-concrete thickness in inches. The temperature conversion factor, TCF,

is given by:

256.1ln754.1 −= tTCF (3.7)

4175.1 <= t forTCF (3.8)

For the analyses reported herein, the 10th percentile fatigue life was used as the basic

performance estimate. This life corresponds to about 10 percent fatigue cracking in the wheel

paths. As verified by sensitivity analysis, incremental agency costs due to off-target construction

(of either inferior or superior quality) are not significantly affected by the chosen performance

percentile (at least within a reasonable range of the 1st to the 20th percentile) (10).

Target values and standard deviations for asphalt content and air-void content are shown

in Table 3.4. This Table also contains an expression for the standard deviation of thickness (10)

used to develop this parameter for the sections analyzed. Table B-1 (Appendix B) contains a

summary of the four pavement sections used in the analyses. These are typical of California

construction for the range in traffic as defined by the Traffic Index (range 7–13).3 Table B-1 also

3 The Traffic Index provides a measure of the applied traffic expressed as ESALs according to the followingrelation: ESALs = 1.2895 × 102(TI)8.2919

10

contains the target standard deviations for thickness for the four sections, computed according to

the equation in Table 3.4.

Table 3.4 Construction Targets

Variable Mean

Total StandardDeviation (IncludingSampling andTesting)

Percent of VarianceAttributed to Materialsand Construction

Asphalt Content (%) 5.0 0.3 40Air-Void Content (%) 7.0 1.5 60Mineral Filler (%) 5.5 0.9 75Fine Aggregate (%) 30.0 3.0 85Asphalt-ConcreteThickness (in.)

4 pavementstructures

0.15 × AC thickness0.69 75

With these targets, Monte Carlo simulations were performed to quantify the effects of

construction quality on simulated in-situ fatigue performance.4 Each investigation employed

either 100,000 simulations (air-void content/relative compaction and asphalt-concrete thickness)

or 200,000 simulations (asphalt content). The levels and ranges used for these simulations are

shown in Table 3.5.

Table 3.5 Levels and Ranges for Variable EvaluatedMean As-Constructed Standard

DeviationVariableLevels Range Levels Range

Asphalt Content 21 4.0 to 6.0 9 0.114 to 0.266Air-Void Content 21 5.00 to 9.75 9 0.648 to 1.596Mineral Filler 21 3.0 to 8.0 9 0.4674 to 1.0906Fine Aggregate 21 24.0 to 36.0 9 1.6596 to 3.8724

Thickness 21 for each of 4pavement sections -1.0 to 1.0 9 4.8% to 11.2%

4 For fatigue, the effects of P200 were not included. Reference (2) describes the basis for the decision.

11

Results, for a structure identified as 11AB20 (Table B-1) are shown in Figures 3.2

through 3.4 illustrating the effects of air-void content, asphalt content, and asphalt concrete

thickness, respectively.

To illustrate the effects of air-void content (as a measure of mix compaction) on agency

costs, the information presented in Figure 3.2 will be utilized. For this example, a maximum

acceptable air-void content has been set at 9.75 percent. Because the air-void content is

considered to be a random variable, some violation of this maximum level during construction is

expected. Figure 3.5 illustrates how the tolerable level of non-compliance affects the

acceptability of various combinations of the average and the standard deviation of air-void

content. As the tolerable level of non-compliance increases, larger and more variable air-void

contents are judged to be acceptable. For the example shown herein, as well as for subsequent

calculations, the tolerable level of non-compliance has been set at 1 percent. This relatively

small (1 percent) failure percentage provides a reasonable probabilistic interpretation to what has

been viewed as a largely deterministic specification.

The influence of as-constructed air-void content on pavement performance is shown in

Figure 3.6. The best performance is associated with small averages and small standard

deviations of air-void content; that is, a consistently well-compacted asphalt concrete layer.

Details of the performance model used to produce Figure 3.6 are summarized in Table 3.6.

The highway agency can reasonably expect typical construction variability (a standard

deviation of air-void content of about 1.2 percent). It can also reasonably expect construction

operations to be in compliance with the specifications, in this case, a 1-percent failure tolerance

of the 9.75 percent air-void requirement. The expected pavement performance in this case,

corresponding to the target air-void content of 7 percent, is about 16,500,000 ESALs (Figure

12

3.7). This is a reasonable target against which to measure both inferior (less than 16,500,00

ESALs) and superior (more than 16,500,000 ESALs) construction.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0

As-constructed average air-void content (%)

Estim

ated

fatig

ue li

fe (m

ultip

le o

f tar

get

ESA

Ls a

t 90%

relia

bilit

y)

0.60%1.20%1.80%

As-constructedstandard

deviation ofair-void

content (%)

Figure 3.2. Effects of as-constructed air-void content on pavement fatigue performance.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

4.0 4.5 5.0 5.5 6.0

As-constructed average asphalt content (%)

Estim

ated

fatig

ue li

fe (m

ultip

le o

f tar

get

ESA

Ls a

t 90%

relia

bilit

y)

0.095%0.190%0.285%


deviation ofasphalt

content (%)

Figure 3.3. Effects of as-constructed asphalt content on pavement fatigue performance.

13

0.0

0.5

1.0

1.5

2.0

2.5

3.0

8.5 9.0 9.5 10.0 10.5

As-constructed average surface thickness (in)

Estim

ated

fatig

ue li

fe (m

ultip

le o

f tar

get

ESA

Ls a

t 90%

relia

bilit

y)

0.31 in0.62 in0.93 in


deviation ofsurface

thickness (in)

Figure 3.4. Effects of as-constructed surface thickness on pavement fatigue performance.

Figure 3.5. Effect of specification failure level on acceptability of mix compaction.

14

Table 3.6 Summary of Parameters in ExampleContext New Pavement Construction

Performance Model

90-percent reliabilityCalifornia coastal temperaturesAverage asphalt content, 5%Standard deviation of asphalt content, 0.19%Standard deviation of thickness, 0.6 in.Coefficient of variation of foundation modulus, 25%

Construction Specification7.0% target air-void content9.75% maximum air-void content1% tolerable failure

Performance Expectation 16,500,000 ESALs

Pavement Structure

9.6-in. asphalt concrete (E = varies, v = 0.40)6-in. aggregate base (E = 25,000 psi, v = 0.45)8.4-in. aggregate subbase (E = 20,000 psi, v = 0.45)Subgrade (E = 12,200 psi, v = 0.50)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5As-constructed average air-void

10

12

14

16

18

20

Million ESALs90%

As-

cons

truc

ted

stan

dard

dev

iatio

n of

air-

void

con

tent

(%)

Figure 3.6. Influence of air-void content on pavement performance.

15

0.00

0.50

1.00

1.50

2.00

2.50

6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5


Expected performance(16.5 million ESALs)

Relative compaction(1% failure at 95% relative compaction)

As-

com

pact

ed s

tand

ard

devi

atio

n of

air-

void

con

tent

(%)

Figure 3.7. Expected pavement performance.

Contractor penalties can reasonably be extracted when the relative compaction

specification is not met and when performance is inferior. This penalty zone is highlighted in

the upper right of Figure 3.8. Contractor bonuses can reasonably be awarded when the relative-

density specification is met and when performance is superior. This bonus zone is highlighted in

the lower left of Figure 3.8. For other cases, no pay adjustment seems to be appropriate.

Although the left, wedge-shaped zone of Figure 3.8 represents conditions having better-than-

expected performance, a bonus should not be awarded because construction fails to meet

specification requirements. The right, wedge-shaped zone of Figure 3.8 represents complying

conditions, but performance fails to meet expectations and, hence, construction does not justify a

contractor bonus. The presence of these two wedge-shaped zones, due in part to the probabilistic

nature of both specification compliance and pavement performance, may explain traditional

problems in trying to link relative-compaction specifications with performance.

16

0.00

0.50

1.00

1.50

2.00

2.50

6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5As-constructed average air-void content (%)

Penalty (fails specificationwith inferior performance)

Bonus (meets specificationwith superior performance)

No pay adjustment(inferior performance)

No pay adjustment(fails specification)

As-

com

pact

ed s

tand

ard

devi

atio

n of

air-

void

con

tent

(%)

Figure 3.8. Influence of air-void content on contractor pay adjustment.

-30

-20

-10

0

10

20

30

50 75 100 125 150As-constructed ESALs (percent of expected ESALs)

Inferiorconstruction

Superiorconstruction

Pres

ent w

orth

of c

hang

e in

reha

bilit

atio

nco

st re

sulti

ng fr

om o

ff-ta

rget

con

stru

ctio

n(p

erce

nt o

f exp

ecte

d co

st)

Figure 3.9. Influence of pavement performance on pay factors.

17

The cost model to be discussed subsequently is based on a comparison between the as-

constructed pavement performance and the expected performance (16.5 × 106 ESALs). A

qualitative indication of the results of the use of the cost model is shown in Figure 3.9.

3.1.3 Permanent Deformation

The performance model used for permanent deformation is a regression equation based

on performance data obtained from the WesTrack experiment (2). This model includes the

effects of air-void content, asphalt content, and aggregate gradation. The resulting equation has

the following form:

( )faPafaVaVPafaa

VaPafaaVaPaaESALs

airairWasp

airWaspairWasprd

⋅⋅+⋅⋅+⋅⋅+⋅+

⋅+⋅+⋅+⋅+⋅+=

2009872

6

25

243210ln

(3.9)

where:

( )ESALsln = natural logarithm of ESALs to specific rut depth (mm),

e.g., rd = 15 mm (0.6 in.)

0a ……. 9a = regression coefficients, Table 3.7

Table 3.7 Regression Coefficients Relating ln(ESALs) to Mix Variables for SpecificLevels of Rutting

Downward Rut Depth (mm)3 6 9 12 15 18

Constant 4.15659 32.1396 35.6119 26.5116 19.6304 15.5941PWasp 4.80344 -4.13639 -4.9073 -1.07049 1.67468 3.32617Vair -0.271222 -0.9128258 -0.695417 -0.655977 -0.608102 -0.57752fa -0.0513972 -0.0561651 -0.060186 -0.066391 -0.0625076 -0.0665384

PWasp2 -0.637872 0.113609 0.174723 -0.18449 -0.430036 -0.574549

Vair2 0.162333 0.0152498 0.0176358 0.0161092 0.0204602 0.0197888

fa2 0.00134321 0.00146158 0.00160422 0.00165989 0.00170736 0.00171777PWasp·Vair 0.0275229 0.143108 0.103099 0.0964891 0.0809674 0.0765997Vair·fa -0.00849295 -0.00903533 -0.010073 -0.00935616 -0.01012 -0.00986111P200·fa 0.00863251 0.00886307 0.00964144 0.00927116 0.00949051 0.00962141R2 0.993 0.991 0.992 0.991 0.996 0.997

18

This equation is based on analysis of both the field performance of 23 test sections which

exhibited rutting (but no fatigue cracking) and the results of simple shear tests on laboratory-

prepared mixes containing gradings representative of the coarse and fine gradings at WesTrack.

Three gradings were used for each of the mixes; the target values and two variations of these

gradings. The ranges for each of the gradings are shown in Figure 3.10. Also shown in this

figure are representative gradings for the Caltrans 19.5-mm (3/4-in.) maximum coarse and

medium gradings. It will be noted that the range of gradings encompasses those likely to be used

for asphalt concrete in California. Reference (2) describes the procedure used to combine the

field and laboratory measured performance data.

Figures 3.11, 3.12, 3.13, and 3.14 illustrate the effects of specific mix parameters for

ESALs to a rut depth of 15 mm (0.6 in.). While other rut depths could be used for these

computations, the 15-mm rut depth was considered reasonable since it is in the range where

remedial action is required.

Using Equation 3.9 and the procedure shown in Figure 3.1b, a series of Monte Carlo

simulations were performed to define relationships between ESALs to 10-percent rutting [15 mm

(0.6 in.) or more] and the various mix parameters shown in Table 3.5. Figures 3.15 and 3.16

illustrate the effects of as-constructed asphalt content and air-void content on the ESALs to 10-

percent rutting (15 mm or more) for a range in standard deviations for each of the parameters.

Figure 3.17 and 3.18, respectively, illustrated the same information but plotted in the form of

asphalt content and air-void content versus as-constructed standard deviation of the associated

parameter. Isolines of ESALs to 10 percent rutting (15 mm or more) are shown in each of the

figures. Also shown are the construction targets.

0

10

20

30

40

50

60

70

80

90

100

2 1/213/41/23/848163050100

Sieve Size

Tota

l Per

cent

Pas

sing

Limits, WesTrack Coarse Low

Coarse High

Limits, WesTrack Fine High

Fine Low

3/4" Medium (middle of limits)

3/4" Coarse (middle of limits)

Figure 3.10. Range of aggregate gradings for WesTrack mixes compared with representative Caltrans gradings.

19

Figure 3.11. Effect of mix variables on simulated ESALs to 15 mm (0.6 in.) rut depth for a range in fine aggregate contents;Vair = 6.5%, P200 = 6.0%.

20

Figure 3.12 Effect of mix variables on simulated ESALs to 15 mm (0.6 in.) rut depth for a range in P200; Vair = 6.5%, fineaggregate = 28%.

21

Figure 3.13. Effect of mix variables on simulated ESALs to 15 mm (0.6 in.) rut depth for a range in air-void contents; P200 =6.0%, fine aggregate = 28%.

22

Figure 3.14. Effect of mix variables on simulated ESALs to 15 mm (0.6 in.) rut depth for a range in asphalt contents; P200 =6.0%, fine aggregate = 28%.

23

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4

As-constructed average aspahlt content (%)

Sim

ulat

ed E

SAL'

s to

10%

rutti

ng (1

5mm

or m

ore

rut d

epth

) exp

rese

d as

fr

actio

n of

targ

et E

SALs

0.1140.190.266

Figure 3.15. Influence of as-constructed asphalt contetn on rutting performance.

24

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5

As-constructed average air void content (%)

Sim

ulat

ed E

SALs

to 1

0% ru

tting

(15

mm

or m

ore

rut d

epth

) exp

ress

ed a

s m

ultip

le o

f tar

get E

SALs

0.61.21.8

Figure 3.16. Influence of as-constructed air-void content on rutting performance.

25

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4As-constructed average asphalt content (%)

As-

cons

truc

ted

stan

dard

dev

iatio

n of

asp

halt

cont

ent

30

25

20

15

10

7

Numbers are million ESALs to 10% rutting (15mm or more)

Constructiontarget

18

Figure 3.17. Influence of as-constructed asphalt content on pavement rutting performance.

26

0.6

0.8

1

1.2

1.4

1.6

1.8

2

5.5 6 6.5 7 7.5 8 8.5


As-

cons

truc

ted

stan

dard

dev

iatio

n of

air-

void

con

tent

13

12 109

811

Numbers are million ESALs to 10% rutting (15 mm or more)

Construction target

Figure 3.18. Influence of as-constructed asphalt content on pavement rutting performance.

27

28

3.2 Cost Model

The performance models yield the 10th percentile in-situ lives for ruts (15 mm depth) and

fatigue cracking (10 percent in wheel paths) for both expected or on-target construction quality

as well as off-target construction quality. The relative performance, RP, the performance input

to the cost model, is computed as follows:

ESALs target-onESALs target-offRP = (3.10)

The first step in the cost model is to determine the off-target pavement life in years, OTY,

that results from the simulated performance differential. Assuming that traffic grows

geometrically, the off-target pavement life is computed as follows:

( )[ ]( )( )g

gRPOTYTY

+−++=

1ln111ln (3.11)

in which g is the annual rate of traffic growth expressed as a decimal and TY is the number of

years of pavement life resulting from on-target construction activity.

The cost model assesses the present worth of moving the first rehabilitation cycle from its

on-target position, TY, to its off-target position, OTY. The net present worth, expressed as a

percentage of the rehabilitation costs (in current-year dollars) is described in the following

paragraphs.

Assume that:

1. C is the resurfacing /rehabilitation cost in current-year dollars;

2. The pavement life, TY, is assumed to be 20 years;

3. r is the annual rate of growth in resurfacing/rehabilitation cost, that is, the

construction cost index;

4. d is the annual discount rate; and

29

5. OTY is the pavement life due to off-target construction.

Then on-target construction will result in:

1. a future cost of C(F/P, r%,20) at the end of the 20-year target period; or

2. an annual equivalent of C(F/P, r%,20)(A/F,d%,20) for 20 years.

where:

F = future worth

P = present worth

A = annuity amount

Off-target construction will result in:

1. a future cost of C(F/P, r%,20) at the end of the off-target period; or

2. an annual equivalent of C(F/P, r%,OTY)(A/F,d%,OTY) for OTY years.

In the event that the OTY is less than the target period, the off-target construction

increases the agency costs over the expected life of 20 years by the present worth of the

difference between these annual cost streams over the OTY period. These costs are illustrated

schematically in Figure 3.19. Their present worth is:

( )( ) ( )( )[ ]( )OTYdAPdFArPFCOTYdFAOTYrPFC %,,20%,,20%,,%,,%,, −

The equation for this expression is:

( )( )

( )( )

( )( )

��

�

+−+

��

��

�

−++−

−++=∆ OTY

OTY

OTY

OTY

dd

dr

drCPW

111

111

111

20

20

(3.12)

When OTY exceeds the target life, the service life for comparison purposes may be set at

either the target life, in this example, 20 years, or the longer OTY. It should be noted that if the

longer period is chosen, it is beneficial to the contractor’s interests.

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Year

Ann

ual c

ost

Annual cost of on-target construction = C (F/P,r%,20) (A/F,d%,20)

Annual cost of off-target construction = C (F/P,r%,OTY) (A/F,d%,OTY)

Annual difference = C (F/P,r%,OTY) (A/F,d%,OTY) -

C (F/P,r%,20) (A/F,d%,20)

Figure 3.19. Schematic illustration of annual costs of on-target and off-target construction.

30

31

While the majority of the pay factor computations to be presented subsequently are based

on the assumption of a target pavement life of 20 years (time to first rehabilitation), some

computations will be presented for other target values (TY) ranging from 10 to 30 years.

4.0 PAY FACTORS

With the information presented in Section 3, it is then possible to determine the

construction pay factors. The following considerations are reflected in the recommended pay

factor schedules included herein:

1. One pay-factor should apply to all new construction; that is, job-specific pay factors

are undesirable

2. The contractor should generally be charged a penalty for inferior construction which

is out of specification, the magnitude of which should equal the full added cost to the

agency for failure to meet the construction target;

3. The contractor should generally be rewarded for superior construction which is within

specification, the magnitude of which should be some fraction of the full added

benefit to the agency resulting from improved pavement performance;

4. Pay factor schedules should incorporate average and standard-deviation categories

consistent with the accuracy within which estimates are determined from field

measurements; and

5. The standard deviation of pay-factor schedules must reflect expected testing and

sampling errors as well as materials/construction variables.

For the actual pay factors developed in this section, bonuses for superior construction and

penalties for inferior construction reflect full agency cost increments. Eventually it will be

32

necessary to make a decision for the fraction of the bonus to be paid for superior construction as

noted in item (3) above. In addition, the examples reflect the following:

1. The sole construction quality effect is the date of first resurfacing/rehabilitation.

2. Both fatigue and rutting distress are reflected in the pay factor schedule. Each entry

in the pay factor schedule is based on the distress mode yielding most beneficial

consequence to the agency, namely, smaller bonus or larger penalty.

3. Pay factors are determined independently for each pay quantity. The combined pay

factor is computed by the following equation:

( )( )( )( )( ) 111111 −+++++= tfamfavac pfpfpfpfpffactorpayCombined (4.1)

in which all pay factors are expressed as decimals. Section 4.4 describes the basis for

this simplified expression for combining pay factors. For convenience, the

definitions which are utilized are summarized as follows:

a) Asphalt content (ac): Percentage of asphalt by weight of total mixture

b) Air-void content (av): Percentage of air voids by volume of total mixture

c) Mineral filler (mf): Aggregate passing 0.074 mm (No. 200) sieve expressed as a

percentage by weight of aggregate

d) Fine aggregate (fa): Aggregate passing 2.36 mm (No. 8) sieve and retained on

0.074 mm (No. 200) sieve expressed as a percentage by weight of aggregate

e) Rutting life: ESALs to 10-percent of rutting with downward depths of 15 mm or

more based on WesTrack performance

f) Fatigue life: ESALs to 10-percent cracking based on Caltrans experience as

summarized by the Caltrans analysis and design model.

33

4.1 Pay Factors—Twenty-Year Expected Pavement Life

The computations in this section, in addition to the assumption of a 20-year expected

pavement life (TY in Equation 3.4) are based on the following cost parameters:

1. 2% annual rate of inflation in resurfacing/rehabilitation cost (r)

2. 2.5% annual rate of traffic growth (g)

3. 5% discount rate (d)

4. Rutting failure results in resurfacing which costs 20% of the cost of new pavement

construction in current-year dollars

5. Fatigue failure results in rehabilitation which costs 50% of the cost of new pavement

construction in current-year dollars.

The cost implications of off-target construction have been determined according to the

procedure described in Section 3.3. Tables 4.1 through 4.4 present the results of the rutting

analysis based on the WesTrack model for rutting. Tables 4.5 through 4.7 present the results of

the fatigue analysis using the California model. Tables 4.5 through 4.7 present the results of the

fatigue analysis using the California model. Tables 4.8 through 4.12 present the results of the

combined analysis showing results most favorable to the agency.

With this information, it is then possible to establish pay-factor tables. These are shown

in Tables 4.13 through 4.17 for each of the five factors considered. The pay factors for air-void

content do not include the effects of either, a) the area where the specification is met but the

performance is inferior to that of the target, or b) the area where the specification is not met but

the performance is superior to that of the target (Figure 3.8).

34

Table 4.1 Effect of off-target asphalt content on future agency resurfacing cost basedon rutting in WesTrack pavements (change expressed as a percent of newpavement construction cost).

As-constructed standard deviation of asphalt content (multiple of 0.19%)As-constructedaverage asphalt

content (%) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.44.0 -13.9 -13.9 -13.8 -13.8 -13.7 -13.6 -13.5 -13.4 -13.34.1 -13.4 -13.4 -13.3 -13.2 -13.1 -13.0 -12.9 -12.8 -12.64.2 -12.8 -12.7 -12.6 -12.5 -12.4 -12.2 -12.1 -11.9 -11.74.3 -12.0 -11.9 -11.8 -11.6 -11.5 -11.3 -11.2 -10.9 -10.84.4 -11.1 -11.0 -10.8 -10.7 -10.5 -10.3 -10.0 -9.8 -9.54.5 -10.0 -9.9 -9.6 -9.5 -9.2 -9.0 -8.7 -8.5 -8.14.6 -8.7 -8.5 -8.3 -8.1 -7.8 -7.5 -7.2 -6.9 -6.54.7 -7.2 -7.0 -6.7 -6.5 -6.2 -5.8 -5.5 -5.0 -4.74.8 -5.5 -5.3 -4.9 -4.7 -4.3 -3.9 -3.5 -3.1 -2.64.9 -3.7 -3.3 -3.0 -2.6 -2.2 -1.8 -1.3 -0.9 -0.45.0 -1.6 -1.2 -0.9 -0.4 0.0 0.5 0.9 1.5 2.05.1 0.7 1.0 1.5 1.9 2.3 2.8 3.4 3.9 4.45.2 3.0 3.3 3.8 4.2 4.8 5.2 5.8 6.2 6.85.3 5.3 5.7 6.1 6.6 7.1 7.6 8.1 8.5 9.05.4 7.6 8.0 8.5 8.9 9.3 9.8 10.2 10.7 11.15.5 9.8 10.2 10.6 10.9 11.4 11.8 12.2 12.6 13.15.6 11.8 12.1 12.5 12.9 13.2 13.6 14.0 14.3 14.75.7 13.5 13.9 14.2 14.5 14.8 15.2 15.4 15.8 16.05.8 15.1 15.3 15.7 15.9 16.2 16.4 16.7 16.9 17.25.9 16.4 16.6 16.8 17.1 17.3 17.5 17.7 17.9 18.16.0 17.4 17.6 17.8 18.0 18.2 18.3 18.5 18.6 18.7

35

Table 4.2 Effect of off-target air-void content on future agency resurfacing cost basedon rutting in WesTrack pavement (change expressed as a percent of newpavement construction cost).

As-constructed standard deviation of relativecompaction (multiple of 1.2%)As-constructed air-

void content (%)0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

5.00 -5.1 -5.0 -4.9 -4.8 -4.6 -4.3 -4.3 -4.0 -3.85.25 -4.5 -4.4 -4.2 -4.2 -3.9 -3.9 -3.6 -3.5 -3.25.50 -3.9 -3.8 -3.7 -3.5 -3.4 -3.2 -3.1 -3.0 -2.75.7 -3.4 -3.2 -3.1 -2.9 -2.8 -2.6 -2.6 -2.4 -2.16.00 -2.7 -2.7 -2.5 -2.4 -2.2 -2.2 -2.0 -1.9 -1.76.25 -2.2 -2.1 -2.0 -1.9 -1.7 -1.6 -1.4 -1.4 -1.26.4 -1.6 -1.5 -1.5 -1.3 -1.3 -1.1 -1.0 -0.9 -0.76.7 -1.1 -1.0 -0.9 -0.9 -0.8 -0.6 -0.6 -0.5 -0.36.9 -0.6 -0.5 -0.4 -0.4 -0.3 -0.3 0.0 0.0 0.17.1 -0.1 0.0 0.0 0.1 0.2 0.3 0.3 0.4 0.57.4 0.3 0.4 0.5 0.6 0.6 0.7 0.7 0.8 0.97.6 0.8 0.8 0.9 0.9 1.0 1.0 1.1 1.2 1.27.85 1.2 1.2 1.3 1.3 1.4 1.4 1.5 1.6 1.58.1 1.6 1.6 1.6 1.7 1.7 1.8 1.8 1.9 1.98.3 2.0 2.0 2.0 2.0 2.1 2.1 2.1 2.2 2.18.6 2.3 2.3 2.4 2.4 2.4 2.4 2.5 2.5 2.48.8 2.6 2.7 2.6 2.7 2.7 2.7 2.7 2.7 2.79.0 2.9 2.9 2.9 2.9 2.9 3.0 2.9 3.0 2.99.3 3.2 3.1 3.2 3.1 3.2 3.1 3.2 3.1 3.19.5 3.4 3.4 3.4 3.4 3.4 3.4 3.4 3.4 3.39.75 3.6 3.6 3.6 3.7 3.5 3.6 3.5 3.6 3.5

36

Table 4.3 Effect of off-target mineral filler on future agency resurfacing cost based onrutting in WesTrack pavement (change expressed as a percent of newpavement construction cost).

As-constructed standard deviation of mineral filler (multiple of 0.7794%)As-constructedaverage mineral

filler (%) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.43.00 6.9 7.0 7.0 7.2 7.3 7.4 7.5 7.7 7.83.25 6.2 6.3 6.4 6.5 6.6 6.7 6.9 7.0 7.13.50 5.5 5.5 5.7 5.8 6.0 6.0 6.2 6.3 6.53.75 4.7 4.9 5.0 5.1 5.2 5.4 5.5 5.7 5.84.00 4.1 4.1 4.2 4.4 4.4 4.6 4.8 5.0 5.04.25 3.4 3.4 3.6 3.6 3.8 3.9 4.0 4.2 4.44.50 2.6 2.7 2.8 2.9 3.0 3.1 3.3 3.4 3.64.75 1.9 2.0 2.0 2.2 2.3 2.5 2.5 2.8 2.85.00 1.1 1.2 1.3 1.4 1.6 1.7 1.8 1.9 2.15.25 0.4 0.4 0.6 0.7 0.8 0.9 1.1 1.2 1.45.50 -0.5 -0.3 -0.3 -0.1 0.0 0.2 0.3 0.5 0.65.75 -1.2 -1.1 -1.0 -0.8 -0.7 -0.6 -0.4 -0.2 -0.16.00 -1.9 -1.8 -1.7 -1.7 -1.4 -1.4 -1.2 -1.1 -0.86.25 -2.7 -2.5 -2.4 -2.3 -2.3 -2.1 -1.9 -1.8 -1.66.50 -3.4 -3.3 -3.2 -3.0 -3.0 -2.8 -2.7 -2.4 -2.46.75 -4.1 -4.0 -3.8 -3.8 -3.7 -3.5 -3.4 -3.3 -3.17.00 -4.8 -4.7 -4.6 -4.5 -4.4 -4.3 -4.1 -4.0 -3.87.25 -5.5 -5.3 -5.4 -5.2 -5.1 -4.9 -4.8 -4.7 -4.57.50 -6.1 -6.1 -6.0 -5.9 -5.8 -5.6 -5.5 -5.3 -5.27.75 -6.8 -6.7 -6.6 -6.6 -6.4 -6.3 -6.1 -6.1 -5.88.00 -7.4 -7.3 -7.3 -7.2 -7.1 -7.0 -6.8 -6.7 -6.6

37

Table 4.4 Effect of off-target fine aggregate on future agency resurfacing cost based onrutting in WesTrack pavement (change expressed as a percent of newpavement construction cost).

As-constructed standard deviation of fineaggregate (multiple of 2.7659%)

As-constructedaverage fine

aggregate (%) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.424.0 0.1 0.1 0.1 0.1 0.0 0.0 0.0 0.0 0.024.6 0.2 0.1 0.2 0.1 0.1 0.0 0.1 0.0 0.125.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.0 0.025.8 0.3 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.026.4 0.3 0.2 0.3 0.2 0.2 0.1 0.1 0.1 0.127.0 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.127.6 0.2 0.2 0.1 0.2 0.1 0.2 0.1 0.1 0.028.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.028.8 0.2 0.1 0.1 0.1 0.1 0.0 0.1 0.0 0.129.4 0.1 0.2 0.1 0.1 0.0 0.0 0.0 0.0 -0.130.0 0.1 0.0 0.1 0.0 0.0 0.0 -0.1 -0.1 -0.130.6 0.0 0.0 0.0 -0.1 0.0 -0.1 -0.1 -0.2 -0.131.2 -0.1 -0.1 -0.2 -0.1 -0.2 -0.1 -0.2 -0.2 -0.231.8 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.3 -0.2 -0.432.4 -0.3 -0.4 -0.3 -0.4 -0.3 -0.4 -0.3 -0.4 -0.433.0 -0.4 -0.4 -0.4 -0.5 -0.4 -0.5 -0.5 -0.5 -0.433.6 -0.6 -0.5 -0.6 -0.6 -0.6 -0.5 -0.7 -0.6 -0.734.2 -0.6 -0.7 -0.7 -0.7 -0.7 -0.7 -0.8 -0.7 -0.834.8 -0.8 -0.8 -0.8 -0.9 -0.8 -0.9 -0.8 -1.0 -0.835.4 -1.1 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.1 -1.136.0 -1.2 -1.2 -1.2 -1.2 -1.2 -1.1 -1.2 -1.1 -1.3

38

Table 4.5 Effect of off-target asphalt content on future agency rehabilitation cost basedon Caltrans fatigue model (change expressed as a percent of new pavementconstruction cost).


content (%) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.44.0 3.2 3.2 3.2 3.2 3.3 3.3 3.3 3.3 3.34.1 2.8 2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.94.2 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.64.3 2.2 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.34.4 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 2.04.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.64.6 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.34.7 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.04.8 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.74.9 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.35.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.05.1 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.35.2 -0.7 -0.7 -0.7 -0.7 -0.7 -0.7 -0.7 -0.7 -0.75.3 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.05.4 -1.4 -1.4 -1.4 -1.4 -1.4 -1.4 -1.4 -1.4 -1.45.5 -1.7 -1.7 -1.7 -1.7 -1.7 -1.7 -1.7 -1.7 -1.75.6 -2.1 -2.1 -2.1 -2.1 -2.1 -2.1 -2.1 -2.0 -2.05.7 -2.5 -2.4 -2.4 -2.4 -2.4 -2.4 -2.4 -2.4 -2.45.8 -2.8 -2.8 -2.8 -2.8 -2.8 -2.7 -2.7 -2.7 -2.75.9 -3.1 -3.1 -3.1 -3.1 -3.1 -3.1 -3.1 -3.1 -3.16.0 -3.5 -3.5 -3.5 -3.5 -3.5 -3.5 -3.5 -3.5 -3.5

39

Table 4.6 Effect of off-target air-void content on future agency rehabilitation costbased on Caltrans fatigue model (change expressed as a percent of newpavement construction cost).


void content (%) 0.6 0.7 0.8 0.9 1.0 1.2 1.3 1.4 1.65.00 -20.4 -19.9 -19.3 -18.7 -18.1 -17.4 -16.7 -15.9 -15.15.25 -18.7 -18.1 -17.5 -16.9 -16.2 -15.4 -14.7 -13.9 -13.05.50 -16.8 -16.2 -15.6 -14.9 -14.2 -13.4 -12.6 -11.8 -10.95.7 -14.9 -14.3 -13.6 -12.9 -12.1 -11.3 -10.5 -9.7 -8.86.00 -12.9 -12.2 -11.5 -10.8 -10.0 -9.2 -8.4 -7.5 -6.66.25 -10.8 -10.1 -9.4 -8.6 -7.9 -7.0 -6.2 -5.3 -4.36.4 -8.7 -8.0 -7.3 -6.5 -5.7 -4.8 -3.9 -3.0 -2.16.7 -6.6 -5.8 -5.1 -4.3 -3.4 -2.6 -1.7 -0.8 0.26.9 -4.4 -3.6 -2.8 -2.0 -1.2 -0.3 0.5 1.5 2.47.1 -2.2 -1.4 -0.6 0.2 1.0 1.9 2.8 3.7 4.67.4 0.1 0.8 1.6 2.4 3.2 4.1 5.0 5.9 6.87.6 2.3 3.0 3.8 4.6 5.4 6.3 7.2 8.0 9.07.85 4.5 5.3 6.0 6.8 7.6 8.4 9.3 10.2 11.18.1 6.7 7.4 8.2 8.9 9.7 10.5 11.4 12.2 13.18.3 8.8 9.6 10.3 11.0 11.8 12.6 13.4 14.2 15.18.6 10.9 11.6 12.4 13.1 13.8 14.6 15.3 16.1 16.98.8 13.0 13.7 14.3 15.0 15.7 16.5 17.2 17.9 18.79.0 15.0 15.6 16.3 16.9 17.6 18.3 19.0 19.7 20.49.3 16.9 17.5 18.1 18.7 19.3 20.0 20.6 21.3 21.99.5 18.7 19.2 19.8 20.4 21.0 21.5 22.1 22.7 23.39.75 20.4 20.9 21.4 21.9 22.5 23.0 23.5 24.1 24.6

40

Table 4.7 Effect of off-target asphalt-concrete thickness on future agency rehabilitationcost based on Caltrans fatigue model (change expressed as a percent of newpavement construction cost).

As-constructed standard deviation of asphalt-concrete thickness (multiple of 8%)

Difference betweenas-measured average

asphalt-concretethickness and design

thickness (in.) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4-1.0 17.7 18.5 19.2 19.9 20.7 21.4 22.3 23.0 23.8-0.9 15.9 16.7 17.4 18.2 19.0 19.8 20.6 21.4 22.3-0.8 14.0 14.8 15.6 16.4 17.2 18.1 18.9 19.8 20.7-0.7 12.0 12.8 13.6 14.5 15.3 16.2 17.1 18.0 18.9-0.6 9.9 10.8 11.6 12.5 13.3 14.2 15.1 16.1 17.1-0.5 7.8 8.6 9.5 10.4 11.3 12.2 13.1 14.1 15.1-0.4 5.6 6.4 7.3 8.2 9.1 10.1 11.0 12.0 13.1-0.3 3.3 4.2 5.0 5.9 6.9 7.9 8.9 9.9 11.0-0.2 1.0 1.9 2.7 3.7 4.6 5.6 6.6 7.6 8.8-0.1 -1.3 -0.5 0.5 1.4 2.3 3.3 4.3 5.3 6.40.0 -3.5 -2.7 -1.9 -1.0 0.0 1.0 2.0 3.0 4.10.1 -5.8 -5.0 -4.1 -3.2 -2.3 -1.4 -0.3 0.7 1.80.2 -7.9 -7.1 -6.3 -5.5 -4.6 -3.6 -2.7 -1.6 -0.60.3 -10.1 -9.3 -8.5 -7.7 -6.8 -5.9 -5.0 -4.0 -2.90.4 -12.1 -11.3 -10.6 -9.8 -8.9 -8.1 -7.1 -6.2 -5.20.5 -14.1 -13.3 -12.6 -11.8 -11.0 -10.2 -9.3 -8.4 -7.40.6 -16.0 -15.3 -14.6 -13.8 -13.0 -12.2 -11.4 -10.5 -9.50.7 -17.9 -17.2 -16.5 -15.8 -15.0 -14.2 -13.4 -12.5 -11.60.8 -20.0 -19.3 -18.5 -17.7 -17.0 -16.2 -15.4 -14.5 -13.70.9 -22.3 -21.4 -20.6 -19.8 -19.0 -18.2 -17.3 -16.5 -15.61.0 -24.8 -23.9 -22.9 -22.0 -21.2 -20.3 -19.4 -18.6 -17.7

41

Table 4.8 Effect of off-target asphalt content on future agencyresurfacing/rehabilitation costs (change expressed as a percent of newpavement construction cost).


content (%) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.44.0 3.2 3.2 3.2 3.2 3.3 3.3 3.3 3.3 3.34.1 2.8 2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.94.2 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.64.3 2.2 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.34.4 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 2.04.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.64.6 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.34.7 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.04.8 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.74.9 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.35.0 0.0 0.0 0.0 0.0 0.0 0.5 0.9 1.5 2.05.1 0.7 1.0 1.5 1.9 2.3 2.8 3.4 3.9 4.45.2 3.0 3.3 3.8 4.2 4.8 5.2 5.8 6.2 6.85.3 5.3 5.7 6.1 6.6 7.1 7.6 8.1 8.5 9.05.4 7.6 8.0 8.5 8.9 9.3 9.8 10.2 10.7 11.15.5 9.8 10.2 10.6 10.9 11.4 11.8 12.2 12.6 13.15.6 11.8 12.1 12.5 12.9 13.2 13.6 14.0 14.3 14.75.7 13.5 13.9 14.2 14.5 14.8 15.2 15.4 15.8 16.05.8 15.1 15.3 15.7 15.9 16.2 16.4 16.7 16.9 17.25.9 16.4 16.6 16.8 17.1 17.3 17.5 17.7 17.9 18.16.0 17.4 17.6 17.8 18.0 18.2 18.3 18.5 18.6 18.7

42

Table 4.9 Effect of off-target air-void content on future agencyresurfacing/rehabilitation costs (change expressed as a percent of newpavement construction cost).


void content (%) 0.6 0.7 0.8 0.9 1.0 1.2 1.3 1.4 1.6100.00 -5.1 -5.0 -4.9 -4.8 -4.6 -4.3 -4.3 -4.0 -3.899.75 -4.5 -4.4 -4.2 -4.2 -3.9 -3.9 -3.6 -3.5 -3.299.50 -3.9 -3.8 -3.7 -3.5 -3.4 -3.2 -3.1 -3.0 -2.799.25 -3.4 -3.2 -3.1 -2.9 -2.8 -2.6 -2.6 -2.4 -2.199.00 -2.7 -2.7 -2.5 -2.4 -2.2 -2.2 -2.0 -1.9 -1.798.75 -2.2 -2.1 -2.0 -1.9 -1.7 -1.6 -1.4 -1.4 -1.298.50 -1.6 -1.5 -1.5 -1.3 -1.3 -1.1 -1.0 -0.9 -0.798.25 -1.1 -1.0 -0.9 -0.9 -0.8 -0.6 -0.6 -0.5 0.298.00 -0.6 -0.5 -0.4 -0.4 -0.3 -0.3 0.5 1.5 2.497.75 -0.1 0.0 0.0 0.2 1.0 1.9 2.8 3.7 4.697.50 0.3 0.8 1.6 2.4 3.2 4.1 5.0 5.9 6.897.25 2.3 3.0 3.8 4.6 5.4 6.3 7.2 8.0 9.097.00 4.5 5.3 6.0 6.8 7.6 8.4 9.3 10.2 11.196.75 6.7 7.4 8.2 8.9 9.7 10.5 11.4 12.2 13.196.50 8.8 9.6 10.3 11.0 11.8 12.6 13.4 14.2 15.196.25 10.9 11.6 12.4 13.1 13.8 14.6 15.3 16.1 16.996.00 13.0 13.7 14.3 15.0 15.7 16.5 17.2 17.9 18.795.75 15.0 15.6 16.3 16.9 17.6 18.3 19.0 19.7 20.495.50 16.9 17.5 18.1 18.7 19.3 20.0 20.6 21.3 21.995.25 18.7 19.2 19.8 20.4 21.0 21.5 22.1 22.7 23.395.00 20.4 20.9 21.4 21.9 22.5 23.0 23.5 24.1 24.6

43

Table 4.10 Effect of off-target mineral filler on future agency resurfacing/rehabilitationcosts (change expressed as a percent of new pavement construction cost).

As-constructed standard deviation of mineral filler (multiple of 0.7794%)As-constructedaverage mineral

filler (%) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.43.00 6.9 7.0 7.0 7.2 7.3 7.4 7.5 7.7 7.83.25 6.2 6.3 6.4 6.5 6.6 6.7 6.9 7.0 7.13.50 5.5 5.5 5.7 5.8 6.0 6.0 6.2 6.3 6.53.75 4.7 4.9 5.0 5.1 5.2 5.4 5.5 5.7 5.84.00 4.1 4.1 4.2 4.4 4.4 4.6 4.8 5.0 5.04.25 3.4 3.4 3.6 3.6 3.8 3.9 4.0 4.2 4.44.50 2.6 2.7 2.8 2.9 3.0 3.1 3.3 3.4 3.64.75 1.9 2.0 2.0 2.2 2.3 2.5 2.5 2.8 2.85.00 1.1 1.2 1.3 1.4 1.6 1.7 1.8 1.9 2.15.25 0.4 0.4 0.6 0.7 0.8 0.9 1.1 1.2 1.45.50 -0.5 -0.3 -0.3 -0.1 0.0 0.2 0.3 0.5 0.65.75 -1.2 -1.1 -1.0 -0.8 -0.7 -0.6 -0.4 -0.2 -0.16.00 -1.9 -1.8 -1.7 -1.7 -1.4 -1.4 -1.2 -1.1 -0.86.25 -2.7 -2.5 -2.4 -2.3 -2.3 -2.1 -1.9 -1.8 -1.66.50 -3.4 -3.3 -3.2 -3.0 -3.0 -2.8 -2.7 -2.4 -2.46.75 -4.1 -4.0 -3.8 -3.8 -3.7 -3.5 -3.4 -3.3 -3.17.00 -4.8 -4.7 -4.6 -4.5 -4.4 -4.3 -4.1 -4.0 -3.87.25 -5.5 -5.3 -5.4 -5.2 -5.1 -4.9 -4.8 -4.7 -4.57.50 -6.1 -6.1 -6.0 -5.9 -5.8 -5.6 -5.5 -5.3 -5.27.75 -6.8 -6.7 -6.6 -6.6 -6.4 -6.3 -6.1 -6.1 -5.88.00 -7.4 -7.3 -7.3 -7.2 -7.1 -7.0 -6.8 -6.7 -6.6

44

Table 4.11 Effect of off-target fine aggregate on future agency resurfacing/rehabilitationcosts (change expressed as a percent of new pavement construction cost).

As-constructed standard deviation of fine aggregate(multiple of 2.7659%)

As-constructedaverage fine

aggregate (%) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.424.0 0.1 0.1 0.1 0.1 0.0 0.0 0.0 0.0 0.024.6 0.2 0.1 0.2 0.1 0.1 0.0 0.1 0.0 0.125.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.0 0.025.8 0.3 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.026.4 0.3 0.2 0.3 0.2 0.2 0.1 0.1 0.1 0.127.0 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.127.6 0.2 0.2 0.1 0.2 0.1 0.2 0.1 0.1 0.028.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.028.8 0.2 0.1 0.1 0.1 0.1 0.0 0.1 0.0 0.129.4 0.1 0.2 0.1 0.1 0.0 0.0 0.0 0.0 -0.130.0 0.1 0.0 0.1 0.0 0.0 0.0 -0.1 -0.1 -0.130.6 0.0 0.0 0.0 -0.1 0.0 -0.1 -0.1 -0.2 -0.131.2 -0.1 -0.1 -0.2 -0.1 -0.2 -0.1 -0.2 -0.2 -0.231.8 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.3 -0.2 -0.432.4 -0.3 -0.4 -0.3 -0.4 -0.3 -0.4 -0.3 -0.4 -0.433.0 -0.4 -0.4 -0.4 -0.5 -0.4 -0.5 -0.5 -0.5 -0.433.6 -0.6 -0.5 -0.6 -0.6 -0.6 -0.5 -0.7 -0.6 -0.734.2 -0.6 -0.7 -0.7 -0.7 -0.7 -0.7 -0.8 -0.7 -0.834.8 -0.8 -0.8 -0.8 -0.9 -0.8 -0.9 -0.8 -1.0 -0.835.4 -1.1 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.1 -1.136.0 -1.2 -1.2 -1.2 -1.2 -1.2 -1.1 -1.2 -1.1 -1.3

45

Table 4.12 Effect of off-target asphalt concrete thickness on future agencyresurfacing/rehabilitation costs (change expressed as a percent of newpavement construction cost).

As-constructed standard deviation ofasphalt-concrete thickness (multiple of 8%)

Difference between as-measured averageasphalt-concrete

thickness and designthickness (in) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

-1.0 17.7 18.5 19.2 19.9 20.7 21.4 22.3 23.0 23.8-0.9 15.9 16.7 17.4 18.2 19.0 19.8 20.6 21.4 22.3-0.8 14.0 14.8 15.6 16.4 17.2 18.1 18.9 19.8 20.7-0.7 12.0 12.8 13.6 14.5 15.3 16.2 17.1 18.0 18.9-0.6 9.9 10.8 11.6 12.5 13.3 14.2 15.1 16.1 17.1-0.5 7.8 8.6 9.5 10.4 11.3 12.2 13.1 14.1 15.1-0.4 5.6 6.4 7.3 8.2 9.1 10.1 11.0 12.0 13.1-0.3 3.3 4.2 5.0 5.9 6.9 7.9 8.9 9.9 11.0-0.2 1.0 1.9 2.7 3.7 4.6 5.6 6.6 7.6 8.8-0.1 -1.3 -0.5 0.5 1.4 2.3 3.3 4.3 5.3 6.40.0 -3.5 -2.7 -1.9 -1.0 0.0 1.0 2.0 3.0 4.10.1 -5.8 -5.0 -4.1 -3.2 -2.3 -1.4 -0.3 0.7 1.80.2 -7.9 -7.1 -6.3 -5.5 -4.6 -3.6 -2.7 -1.6 -0.60.3 -10.1 -9.3 -8.5 -7.7 -6.8 -5.9 -5.0 -4.0 -2.90.4 -12.1 -11.3 -10.6 -9.8 -8.9 -8.1 -7.1 -6.2 -5.20.5 -14.1 -13.3 -12.6 -11.8 -11.0 -10.2 -9.3 -8.4 -7.40.6 -16.0 -15.3 -14.6 -13.8 -13.0 -12.2 -11.4 -10.5 -9.50.7 -17.9 -17.2 -16.5 -15.8 -15.0 -14.2 -13.4 -12.5 -11.60.8 -20.0 -19.3 -18.5 -17.7 -17.0 -16.2 -15.4 -14.5 -13.70.9 -22.3 -21.4 -20.6 -19.8 -19.0 -18.2 -17.3 -16.5 -15.61.0 -24.8 -23.9 -22.9 -22.0 -21.2 -20.3 -19.4 -18.6 -17.7

46

Table 4.13 Contractor pay factors for asphalt content (percentage of futureresurfacing/rehabilitation cost in current-year dollars).

As-measured standard deviation of asphalt content (%)Difference between as-

measured average asphaltcontent and design asphalt

content (%) Below 0.255 0.255 to 0.345 Above 0.345-1.10 to -0.91 -3 -3 -3-0.90 to 0.71 -3 -3 -3-0.70 to -0.51 -2 -2 -2-0.50 to -0.31 -1 -1 -1-0.30 to -0.11 -1 -1 -1-0.10 to 0.09 0 0 -10.10 to 0.29 -3 -5 -60.30 to 0.49 -8 -9 -110.50 to 0.69 -12 -13 -140.70 to 0.89 -15 -16 -170.90 to 1.09 -18 -18 -19

Table 4.14 Contractor pay factors for air-void content (percentage of futureresurfacing/rehabilitation cost in current-year dollars).

As-measured standard deviation of relative compaction (%)As-measured averagerelative compaction (%) Below 1.32 1.32 to 1.78 Above 1.78

100.25 to 99.76 5 5 499.75 to 99.26 4 3 399.25 to 98.76 3 2 298.75 to 98.26 2 1 198.25 to 97.76 1 0 -197.75 to 97.26 -1 -3 -697.25 to 96.76 -5 -8 -1096.75 to 96.26 -10 -12 -1496.25 to 95.76 -14 -16 -1895.75 to 95.26 -17 -19 -2195.25 to 94.76 -21 -22 -24

47

Table 4.15 Contractor pay factors for asphalt-concrete thickness (percentage of futureresurfacing/rehabilitation cost in current-year dollars).

As-measured standard deviation ofasphalt-concrete thickness (%)

Difference between as-measured average asphalt-

concrete thickness anddesign thickness (in) Below 7.85 7.85 to 10.62 Above 10.62

-1.10 to -0.89 -18 -21 -23-0.90 to -0.69 -15 -17 -20-0.70 to -0.49 -11 -13 -16-0.50 to -0.29 -6 -9 -12-0.30 to -0.09 -2 -5 -8-0.10 to 0.09 3 0 -30.10 to 0.29 7 5 20.30 to 0.49 11 9 60.50 to 0.69 15 13 100.70 to 0.89 19 17 150.90 to 1.09 24 21 19

Table 4.16 Contractor pay factors for mineral filler (percentage of futureresurfacing/rehabilitation cost in current-year dollars).

As-measured standard deviation of mineral filler (%)Difference between as-measuredaverage mineral filler and design

mineral filler (%) Below 0.765 0.765 to 1.035 Above 1.035-2.75 to -2.26 -7 -7 -8-2.25 to -1.76 -6 -6 -6-1.75 to - 1.26 -4 -4 -5-1.25 to -0.76 -3 -3 -3-0.75 to -0.26 -1 -2 -2-0.25 to 0.24 0 0 00.25 to 0.74 2 1 10.75 to 1.24 3 3 31.25 to 1.74 5 4 41.75 to 2.24 6 6 52.25 to 2.74 7 7 7

48

Table 4.17 Contractor pay factors for fine aggregate (percentage of futureresurfacing/rehabilitation cost in current-year dollars).

As-measured standard deviation of fine aggregate (%)Difference between as-measured average fine

aggregate and design fineaggregate (%) Below 2.55 2.55 to 3.45 Above 3.45

-6.6 to - 5.5 0 0 0-5.4 to -4.3 0 0 0-4.2 to -3.1 0 0 0-3.0 to -1.9 0 0 0-1.8 to -0.7 0 0 0-0.6 to 0.5 0 0 00.6 to 1.7 0 0 01.8 to 2.9 0 0 03.0 to 4.1 1 1 14.2 to 5.3 1 1 15.4 to 6.5 1 1 1

4.2 Pay Factors—Influence of Expected Pavement Life and Cost Parameters

The pay factors computed in the previous section are based on what are considered

“reasonable” cost parameters and a target design life of 20 years.

In discussions with Caltrans staff, some different parameters have been suggested. For

example, Caltrans currently uses an annual rate of inflation for pavement costs of 3.5 percent. In

addition, a variety of design periods are used:

Category Design PeriodNew pavement 40Rehabilitated pavement (urban) 30-35Rehabilitated pavement (rural) 10-20CapM5 5

The influence of some of these parameters on pay factors is analyzed in this section.

The first study involved changing the target pavement life to 10 years and increasing the

annual inflation rate to 3.5 percent. The other factors were the same as used in Section 4.1., i.e.,

5 CapM refers to Capital Preventative Maintenance projects

49

g = 2.5 percent, d = 5 percent, and the cost of rehabilitation for rutting and fatigue were 20 and

50 percent of new pavement construction, respectively.

Tables 4.18 through 4.20 show the cost implications of off-target construction for both

rutting and fatigue and their combined values. Table 4.21 summarizes the pay factors for asphalt

content. It will be noted that the negative pay factors for low asphalt content are larger than

those for the 20-year target pavement life (Table 4.13) whereas the negative factors for high

asphalt content are similar to those in the table.

Tables 4.22 through 4.25 show the contractor pay factors for air-void content, AC

thickness, mineral filler, and fine aggregate. Of particular significance are the more severe pay

factors associated with pavement thickness variations for the 10-year target life as compared to

the 20-year life. The effects of aggregate grading on pay factors is relatively little influenced by

pavement life, i.e., 10 years versus 20 years.

Tables 4.26 through 4.35 illustrate the same pay factor determination for 30 and 20 year

target lives using an annual inflation rate of 3.5 percent. It will be noted that the inflation rate

has the most significant impact on pay factors for AC thickness (Table 4.23 versus Table 4.28

versus Table 4.33).

4.3 Comparison of Current Caltrans Pay Factors with Those Obtained fromPerformance Models Presented Herein

Caltrans personnel supplied information for an overlay project on SR-299 in Trinity

County between Salyer and Del Loma.(11) Construction started in June 1999 and was

completed in March 2000. In July 1999 bleeding was observed in the eastbound lane. During

the period July 7 to July 23, 1999 the contractor placed an average of 2300 tonnes per day.

Table 4.36 lists the pay factors and daily AC tonnage for this period. It will be noted that the

50

Table 4.18 Effect of off-target asphalt content on future agency resurfacing cost basedon rutting in WesTrack pavements (change expressed as a percent of newpavement construction cost); target life = 10 years, r = 3.5 percent


content (%) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.44.0 -27.0 -26.9 -26.7 -26.5 -26.3 -26.0 -25.8 -25.4 -25.34.1 -25.5 -25.4 -25.1 -24.9 -24.6 -24.4 -24.0 -23.7 -23.34.2 -23.8 -23.6 -23.3 -23.0 -22.7 -22.4 -22.0 -21.7 -21.24.3 -21.8 -21.5 -21.3 -20.9 -20.6 -20.1 -19.8 -19.3 -18.94.4 -19.6 -19.3 -18.9 -18.6 -18.2 -17.7 -17.2 -16.7 -16.14.5 -17.1 -16.8 -16.4 -16.0 -15.4 -15.1 -14.4 -14.0 -13.24.6 -14.5 -14.0 -13.7 -13.2 -12.7 -12.1 -11.5 -10.9 -10.34.7 -11.5 -11.2 -10.6 -10.1 -9.6 -9.0 -8.4 -7.6 -7.14.8 -8.5 -8.1 -7.5 -7.0 -6.4 -5.8 -5.1 -4.5 -3.74.9 -5.4 -4.9 -4.4 -3.7 -3.2 -2.5 -1.8 -1.2 -0.55.0 -2.2 -1.7 -1.2 -0.6 0.0 0.7 1.2 2.0 2.65.1 0.9 1.3 1.9 2.5 3.0 3.6 4.3 4.9 5.65.2 3.8 4.3 4.8 5.3 6.0 6.4 7.1 7.6 8.35.3 6.6 7.1 7.5 8.0 8.5 9.0 9.6 10.0 10.55.4 9.1 9.5 10.0 10.4 10.8 11.3 11.7 12.2 12.65.5 11.3 11.7 12.1 12.4 12.9 13.2 13.6 13.9 14.35.6 13.2 13.5 13.8 14.2 14.5 14.8 15.1 15.5 15.75.7 14.8 15.1 15.3 15.6 15.9 16.2 16.4 16.7 16.95.8 16.1 16.3 16.6 16.8 17.0 17.2 17.4 17.6 17.85.9 17.2 17.4 17.5 17.7 17.9 18.1 18.2 18.4 18.56.0 18.0 18.2 18.3 18.5 18.6 18.7 18.8 18.9 19.0

51

Table 4.19 Effect of off-target asphalt content on future agency rehabilitation cost basedon Caltrans fatigue model (change expressed as a percent of new pavementconstruction cost); target life = 10 years, r = 3.5 percent.


content (%) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.44.0 16.4 16.4 16.4 16.4 16.7 16.7 16.7 16.7 16.74.1 14.6 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.94.2 13.0 13.0 13.0 13.0 13.0 13.3 13.3 13.3 13.34.3 11.2 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.54.4 9.7 9.7 9.7 9.7 9.7 9.7 9.7 9.7 10.04.5 8.0 8.0 8.0 8.3 8.3 8.3 8.3 8.3 8.34.6 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.54.7 4.8 4.8 4.8 4.8 4.8 4.8 4.8 4.8 5.14.8 3.1 3.1 3.1 3.1 3.1 3.4 3.4 3.4 3.44.9 1.4 1.4 1.7 1.7 1.7 1.7 1.7 1.7 1.75.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.05.1 -1.7 -1.7 -1.7 -1.7 -1.7 -1.7 -1.7 -1.7 -1.75.2 -3.3 -3.3 -3.3 -3.3 -3.3 -3.3 -3.3 -3.3 -3.35.3 -4.9 -4.9 -4.9 -4.9 -4.9 -4.9 -4.9 -4.9 -4.95.4 -6.7 -6.7 -6.5 -6.5 -6.5 -6.5 -6.5 -6.5 -6.55.5 -8.3 -8.3 -8.3 -8.3 -8.1 -8.1 -8.1 -8.1 -8.15.6 -9.9 -9.9 -9.9 -9.9 -9.9 -9.9 -9.9 -9.6 -9.65.7 -11.6 -11.4 -11.4 -11.4 -11.4 -11.4 -11.4 -11.4 -11.45.8 -13.2 -13.2 -13.2 -13.2 -13.2 -12.9 -12.9 -12.9 -12.95.9 -14.6 -14.6 -14.6 -14.6 -14.6 -14.6 -14.6 -14.6 -14.66.0 -16.4 -16.4 -16.4 -16.4 -16.4 -16.4 -16.1 -16.1 -16.1

52

Table 4.20 Effect of off-target asphalt content on future agencyresurfacing/rehabilitation costs (change expressed as a percent of newpavement construction cost); target life = 10 years, r = 3.5 percent.


content (%) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.44.0 16.4 16.4 16.4 16.4 16.7 16.7 16.7 16.7 16.74.1 14.6 14.9 14.9 14.9 14.9 14.9 14.9 14.9 14.94.2 13.0 13.0 13.0 13.0 13.0 13.3 13.3 13.3 13.34.3 11.2 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.54.4 9.7 9.7 9.7 9.7 9.7 9.7 9.7 9.7 10.04.5 8.0 8.0 8.0 8.3 8.3 8.3 8.3 8.3 8.34.6 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.54.7 4.8 4.8 4.8 4.8 4.8 4.8 4.8 4.8 5.14.8 3.1 3.1 3.1 3.1 3.1 3.4 3.4 3.4 3.44.9 1.4 1.4 1.7 1.7 1.7 1.7 1.7 1.7 1.75.0 0.0 0.0 0.0 0.0 0.0 0.7 1.2 2.0 2.65.1 0.9 1.3 1.9 2.5 3.0 3.6 4.3 4.9 5.65.2 3.8 4.3 4.8 5.3 6.0 6.4 7.1 7.6 8.35.3 6.6 7.1 7.5 8.0 8.5 9.0 9.6 10.0 10.55.4 9.1 9.5 10.0 10.4 10.8 11.3 11.7 12.2 12.65.5 11.3 11.7 12.1 12.4 12.9 13.2 13.6 13.9 14.35.6 13.2 13.5 13.8 14.2 14.5 14.8 15.1 15.5 15.75.7 14.8 15.1 15.3 15.6 15.9 16.2 16.4 16.7 16.95.8 16.1 16.3 16.6 16.8 17.0 17.2 17.4 17.6 17.85.9 17.2 17.4 17.5 17.7 17.9 18.1 18.2 18.4 18.56.0 18.0 18.2 18.3 18.5 18.6 18.7 18.8 18.9 19.0

53

Table 4.21 Contractor pay factors for asphalt content (percentage of futureresurfacing/rehabilitation cost in current-year dollars); target life = 10 years,r = 3.5 percent.




Table 4.22 Contractor pay factors for air-void content (percentage of futureresurfacing/rehabilitation cost in current-year dollars); target life = 10 years,r = 3.5 percent.

As-measured standard deviation of relative compaction (%)As-measured average air-void content (%) Below 1.32 1.32 to 1.78 Above 1.78


54

Table 4.23 Contractor pay factors for asphalt-concrete thickness (percentage of futureresurfacing/rehabilitation cost in current-year dollars); target life = 10 years,r = 3.5 percent.





Table 4.24 Contractor pay factors for mineral filler (percentage of futureresurfacing/rehabilitation cost in current-year dollars); target life = 10 years,r = 3.5 percent.


mineral filler (%) Below 0.765 0.765 to 1.035 Above 1.035-2.75 to -2.26 -8 -9 -9-2.25 to -1.76 -7 -7 -8-1.75 to - 1.26 -5 -6 -6-1.25 to -0.76 -4 -4 -4-0.75 to -0.26 -2 -2 -3-0.25 to 0.24 0 0 -10.25 to 0.74 3 2 10.75 to 1.24 5 4 41.25 to 1.74 7 7 61.75 to 2.24 9 9 82.25 to 2.74 12 11 11

55

Table 4.25 Contractor pay factors for fine aggregate (percentage of futureresurfacing/rehabilitation cost in current-year dollars); target life = 10 years,r = 3.5 percent.



-6.6 to -5.5 0 0 0-5.4 to -4.3 0 0 0-4.2 to -3.1 0 0 0-3.0 to -1.9 0 0 0-1.8 to -0.7 0 0 0-0.6 to 0.5 0 0 00.6 to 1.7 0 0 01.8 to 2.9 0 0 13.0 to 4.1 1 1 14.2 to 5.3 1 1 15.4 to 6.5 2 2 2





56









57

Table 4.29 Contractor pay factors for mineral filler (percentage of futureresurfacing/rehabilitation cost in current-year dollars); target life = 30 years,r = 3.5 percent.







58








59






Table 4.34 Contractor pay factors for mineral filler (percentage of futureresurfacing/rehabilitation cost in current-year dollars) ; target life = 20years, r = 3.5 percent.



60





Table 4.36 Pay Factor Summary—Overlay Project, SR 299, Trinity County, July 1999AC Pay Factor and Tonnes Summary

Date Day Sample Pay Factor Daily Tonnes Total Tonnes07/06/99 Tue 1-5 1.0087 2,093 2,09307/07/99 Wed 6-13 1.0447 3,569 5,66207/08/99 Thu 14-20 1.0407 3,186 8,84907/09/99 Fri 21-28 1.0367 3,547 12,39507/12/99 Mon 29-36 1.0311 3,482 15,87707/13/99 Tue 37-40 1.0341 1,838 17,71507/14/99 Wed 41-47 1.0291 3,347 21,06207/16/99 Fri 48-53 1.0281 2,866 23,92807/19/99 Mon 54-61 1.0311 3,507 27,43507/20/99 Tue 62-68 1.0291 2,930 30,36407/21/99 Wed 69-76 1.0341 3,590 33,95407/22/99 Thu 77-79 1.0371 1,635 35,59007/23/99 Fri 80-83 1.0371 1,606 37,195

61

contractor received a bonus for the project even though a segment of the resurfacing exhibited

bleeding. The project thus provided an opportunity to compare pay factors developed in Section

4.2 with those currently used in the Caltrans Specifications Quality Control/Quality Assurance

for Asphalt Concrete.

From an analysis of the mix data for the project which had been supplied by Caltrans, the

mix tends to be a “critical” mix; that is, small increases in asphalt content lead to significant

decreases in mix stability as measured by the stabilometer. It was also noted that the contractor

appeared to operate on the high side of the binder content range.

Using data prepared by one of the contractor’s testing laboratories (June 8, 1999), a

significant reduction in stability occurs in the range 5.0 to 5.5 percent binder content, a reduction

from 46 to 23, with a corresponding reduction in air-void content from 2.6 to 1.5 percent. These

air-void content determinations are based on the computation procedure described in CA Test

Method 367 using aggregate specific gravities determined in accordance with CA Test Methods

206 and 207.

With a critical mix, if the original Hveem procedure were followed, one would back off

0.5 percent from the binder content corresponding (in this case) to S=37. This would suggest a

binder content of 4.7 percent as the target value. Secondly, a stricter control in binder content

would be placed, that is ±0.3 percent.

Data from tests on field cores indicate binder contents, reported in the District 3 Materials

Lab memo data August 1999, to be on the high side resulting in low stabilometer values

associated with low air-void contents.

Using pay factors reported in Section 4.2 and considering only binder content, a pay

factor of about 0.9 would be obtained. This is based on an actual value 0.4 percent above the

62

actual target value of 4.8 percent and a standard deviation of 0.3 percent resulting in an off-target

life of about 4 years. If the standard deviation in binder content were larger or the actual value

larger than that stated, the pay factor would be further reduced. The effects of the improved

relative compaction would tend to increase the factor slightly; however, this would not overcome

the potential for bleeding such as was observed on some of the sections.

It must be emphasized that the pay factor determinations (Section .42) are based on a 10-

year life for a mix constructed at the target value for binder content and the rutting performance

model developed from the WesTrack data.

If the same target life was used, i.e., 10 years and the off-target life was assumed to be 1

year, then the pay factor used would be substantially less than the value of 0.9 noted above.

4.4 Combined Pay Factors

Combined pay factors can be determined from the information presented in, for example,

Tables 4.13 through 4.17 using Equation 4.1. This equation results from a series of simulations

reported in Reference (10), as discussed below.

Considering only fatigue performance, 10 conditions (five for air-void content and five

for thickness), which individually resulted in a “constant” pay factor of about –20 percent, were

selected. The combination effects from the simulations are shown in Table 4.37. Interestingly,

the combination pay factor is about –36 percent, when both air-void content and thickness are

off-target with individual pay factors of –20 percent each. This suggests the possibility that the

combination pay factor as a decimal fraction, cpf, might be expressed as follows:

( )( ) 111 −++= tav pfpfcpf (4.2)

in which the individual pay factors are expressed as decimal fractions instead of percents.

63

To further investigate this possibility, the simulations of Table 4.38 were performed.

Again, the focus was on air-void content/relative compaction and thickness because these are the

dominant parameters of interest. This time, however, the as-constructed conditions were

selected to yield large ranges in individual pay factors including bonuses (instead of –20

percent). Next, calculations for comparable conditions using the above equation yielded results

summarized in Table 4.39. Although there is one notable difference at one extreme (96.1 percent

versus 69.1 percent), results of the combined simulations (Table 4.38) and the computations

(Table 4.39) are in remarkable agreement. As a result, Equation 4.2 seems suitable for

determining pay factors for combined conditions. An extension to include asphalt content yields

the following recommendation for computing combined contractor pay factors:

( )( )( ) 1111 −+++= tacav pfpfpfcpf (4.3)

Equation 4.3, following completion of the WesTrack analyses, was extended to include

the effects of aggregate gradation as follows:

( )( )( )( )( ) 111111)( −+++++= tfamfavac pfpfpfpfpfCPFFactorPayCombined (4.4)

Consider the following using Tables 4.13 through 4.17. A contractor has compacted a

mix to an air-void content of 5.0 percent (target value = 7 percent) with standard deviation of 1.6

percent; the asphalt content was 0.5 percent above target with a standard deviation of 0.4

percent; the mineral filler was 0.5 percent above target with a standard deviation of 1.2 percent;

the fine aggregate was on target with a standard deviation of 3 percent; and the thickness was 0.3

in. below target with a standard deviation of 8.5 percent.

For these conditions, the combined pay factor is:

( )( )( )( )( ) %8383.008.010101.0104.0114.01 orCPF =−−−−−=

64

Table 4.37 Pay Factors for Combination Conditions (from Simulations) (Conditions Setto Yield Individual Pay Factors of About –20 Percent)

Average Air-Void Content (%)Surface Thickness (in.) 7.000 7.755 8.040 8.325 8.610Standard Deviation of Air-Void Content (%)Average Standard

Deviation 1.200 1.686 1.378 1.028 0.6379.6 0.620 0.0 -20.3 -19.6 -19.7 -20.38.8 0.353 -21.0 -37.8 -37.2 -36.5 -36.09.0 0.587 -20.7 -36.9 -36.5 -36.6 -36.89.2 0.791 -20.7 -36.2 -36.3 -36.7 -37.49.4 0.975 -20.6 -35.2 -36.2 -36.9 -38.2

Table 4.38 Pay Factors for Combination Conditions (from Simulations) (Conditions Setto Yield Varying Individual Pay Factors)

Average Air-Void Content (%)Surface Thickness (in.) 5.95 7.09 7.00 7.09 8.80Standard Deviation of Air-Void Content (%)

.0570 .0570 1.200 1.710 1.520Individual Pay Factor

Average StandardDeviation

IndividualPay Factor

0.262 0.060 0.000 -0.097 -0.32010.5 0.60 0.340 96.1 41.6 33.9 23.5 -2.89.9 0.60 0.123 39.3 18.2 12.2 2.5 -22.89.6 0.62 0.000 23.2 6.3 0.0 -9.5 -32.09.3 0.70 -0.134 11.3 -8.6 -13.7 -22.5 -41.18.5 0.80 -0.408 -24.0 -38.5 -41.0 -45.3 -56.5

Table 4.39 Pay Factors for Combination Conditions (from Calculations) (Conditions Setto Yield Varying Individual Pay Factors)

Average Air-Void Content (%)Surface Thickness (in.) 5.95 7.09 7.00 7.09 8.80Standard Deviation of Air-Void Content (%)

.0570 .0570 1.200 1.710 1.520Individual Pay Factor

Average StandardDeviation

IndividualPay Factor

0.262 0.060 0.000 -0.097 -0.32010.5 0.60 0.340 69.1 42.0 34.0 21.0 -8.99.9 0.60 0.123 41.7 19.0 12.3 1.4 -23.69.6 0.62 0.000 26.2 6.0 0.0 -9.7 -32.09.3 0.70 -0.134 9.3 -8.2 -13.4 -21.8 -41.18.5 0.80 -0.408 -25.3 -37.2 -40.8 -46.5 -59.7

65

It is possible to prepare a combined pay factor table like that shown in Reference (10).

However, with the five variables of Equation (4.4), it is recommended that Equation (4.4) be

used to calculate the combined pay factor, particularly if pay factors are computed based on the

results of one-day or shorter operations, even though the paving project may have a duration of

many days.

5.0 DISCUSSION

The approach presented herein should be applicable to virtually any type of hot mix,

although as a check, additional laboratory testing would be required. It is likely that both

bonuses and penalties may be understated because only the first rehabilitation cycle is

considered. Nevertheless, understated penalties/bonuses are likely to be more appropriate than

overstated ones for pilot or demonstration use at this time.

The pay factor tables contained herein reflect a full bonus for superior construction and a

full penalty for inferior construction. Based on current practice, the bonus to be awarded should

not exceed some prescribed level somewhat less than the maximum values shown herein.

Currently, the upper limit for Caltrans is a bonus of 5 percent. Also, as noted in Section 4.1, the

pay factors for air-void content do not include the effects of either area, Figure 3.8, where the

specification is met but the performance is inferior to that of the target or the area where the

specification is not met but the performance is superior to that of the target.

Recognizing some of the limitation noted herein, the pay factors provide a reasonable

starting point for hot mix asphalt concrete construction considering the combined effects of

rutting and fatigue cracking or only one of the distress modes if that is considered to be suitable.

For example, if only rutting is to be considered, for a target life of 20 years, the pay

factors should include those for asphalt content, air-void content, and aggregate gradation shown

66

in Tables 4.13, 4.14, 4.16, and 4.17. For fatigue for the 20-year target, the pay factors for asphalt

content, air-void content, and thickness shown in Tables 4.13 through 4.15 should be included.

(N.B. These tables are based on an inflation rate of 2.5 percent and rehabilitation costs which are

0.2 times the initial construction cost for rutting and 0.5 time the cost for fatigue.)

For an inflation rate of 3.5 percent, Tables 4.21 through 4.25 contain combined pay

factors for a 10-year target life while Tables 4.26 through 4.30 and 4.31 through 4.35 contain the

same information for target lives of 30 and 20 years, respectively. It will be noted that the pay

factors for the target life of 30 years are equal or less than those for 20 and 10 year periods.

It must be emphasized that the development of appropriate pay-factor schedules must be

viewed as an incremental process evolving over some time frame. Among future refinements

that can be considered are the following:

1. Incorporation of ride quality as a product of the construction process;

2. Inclusion, if desired, of maintenance and user costs;

3. Extension to include rehabilitation activities; and

4. Extension to include cement concrete pavements.

Moving from concept to practice is possible at this time. However, a number of

questions must be answered by Caltrans: Does interest focus on new pavements and/or overlays

and can initial consideration be limited to asphalt concrete applications as described herein?

Help is needed from Caltrans staff to validate the variances that have been utilized herein to

insure that they are representative of current construction practice. In addition to the example

presented in Section 4.3, a number of past construction projects should be reviewed to evaluate

their distribution relative to any pay-factor schedule that is ultimately proposed.

Other questions include:

67

1. Are the parameters used herein those most suitable for Caltrans usage?

2. Is the recommended procedure for displaying individual pay factors and the

procedure used to develop combined pay factors suitable?

3. How does this approach for pay factor determination relate to the QC/QA program

envisioned by Caltrans, including other construction-quality considerations?

4. How best can the CAL/APT program support the Caltrans initiative for demonstrating

a new or modified approach for pay factors for asphalt concrete construction and

what is the timeline for such a program?

6.0 REFERENCES

1. Harvey, J. T., J. Roesler, N. F. Coetzee, and C. L. Monismith. Caltrans AcceleratedPavement Test Program, Summary Report Six Year Period: 1994–2000. Prepared for theCalifornia Department of Transportation, Pavement Research Center, University ofCalifornia, Berkeley, June 2000, 112 pp.

2. Monismith, C. L., J. A. Deacon, and J. T. Harvey. WesTrack: Performance Models forPermanent Deformation and Fatigue. Pavement Research Center, University of California,Berkeley, June 2000, 373 pp.

3. Deacon, J. A., A. A. Tayebali, J. S. Coplantz, F. N. Finn, and C. L. Monsmith. FatigueResponse of Asphalt-Aggregate Mixtures: Part III, Mix Design and Analysis. Report SHRPA-404, Strategic Highway Research Program, National Research Council, Washington, D.C., 1994, 309 pp.

4. Deacon, J. A., J. S. Coplantz, A. A. Tayebali, and C. L. Monismith. “TemperatureConsiderations in Asphalt-Aggregate Mixture Analysis and Design.” Research Record 1454.Transportation Research Board, Washington, D. C., pp. 97-112.

5. Harvey, J. T., J. A. Deacon, B. W. Tsai, and C. L. Monismith. Fatigue Performance ofAsphalt Concrete Mixes and Its Relationship to Asphalt Concrete Pavement Performance inCalifornia. University of California, Berkeley, Institute of Transportation Studies, AsphaltResearch Program, CAL/APT Program, 1995, 188 pp.

6. Harvey, J. T., J. A. Deacon, A. A. Tayebali, R. B. Leahy, and C. L. Monismith. “AReliability-Based Mix Design and Analysis System for Mitigating Fatigue Distress.”Proceedings. 8th International Conference on Asphalt Pavements. University ofWashington, Seattle, August 1997, I:301-323.

68

7. Epps, J. Accelerated Field Test of Performance-Related Specifications for Hot-Mix AsphaltConstruction—Task G, Interim Report. Submitted to the Federal Highway Administration.Nevada Automotive Test Center. Chapter 12. 1996.

8. Benson, P. Comparison of End-Result and Method Specifications for Managing Quality.Paper presented at the 74th Transportation Research Board Annual Meeting, Washington, D.C.

9. Granley, E. “Part 4—Variations of Bituminous Construction.” Public Roads. Vol. 35, No. 9.1969.

10. Deacon, J. A., C. L. Monismith, and J. T. Harvey. Pay Factors for Asphalt-ConcreteConstruction: Effect of Construction Quality on Agency Costs. TM-UCB-CAL/APT-97-1.Pavement Research Center, Institute of Transportation Studies, University of California,Berkeley, 47 pp., April 1997.

11. Dietz, J. Various correspondence, September–November 2000 regarding asphalt concreteoverlay, SR-299, Trinity County, California.

12. Federal Highway Administration (FHWA). LTPP Analysis: Putting the Data to Work.FHWA-RD-99-169, USDOT, FHWA, Washington, D. C., 1999, 21 pp.

13. American Association of State Highway and Transportation Officials (AASHTO). Guide forDesign of Pavement Structures. Washington, D. C., 1993.

14. Tayebali, A. A., J. A. Deacon, J. S. Coplantz, J. T. Harvey, and C. L. Monismith. FatigueResponse of Asphalt-Aggregate Mixes. Report SHRP-A-404. Strategic Highway ResearchProgram, National Research Council, Washington, D. C., 1994, 309 pp.

15. Puangchit, P., R. G. Hicks, J. E. Wilson, and C. A. Bell. Impact of Variation in MaterialProperties on Asphalt Pavement. Oregon Department of Transportation, May 1982, 152 pp.

16. Larson, G. and B. Dempsey. ICM Software. Enhanced Integrated Climatic Model Version2.0 (ICM). University of Illinois, Urbana, Illinois, 1997.

17. Sousa, J. B., J. A. Deacon, S. Weissman, J. T. Harvey, C. L. Monismith. FatiguePerformance of Asphalt Concrete Mixes and Its Relationship to Asphalt Concrete PavementPerformance in California. Asphalt Research Program, CAL/APT Program, Institute ofTransportation Studies, University of California, Berkeley, 1996.

18. Shook, J. F., F. N. Finn, M. W. Wticzak, and C. L. Monismith. “Thickness and Design ofAsphalt Pavements The Asphalt Institute Method.” Proceedings. Fifth InternationalConference on the Structural Design of Asphalt Pavement, University of Michigan and DelftUniversity of Technology, August 1982, Vol. 2, pp. 17-44.

69

APPENDIX A: RELIABILITY AND VARIABILITY CONSIDERATIONS

To provide an acceptable level of risk in asphalt mix design and pavement performance

without excessive cost, reliability analysis can be used. Reliability, as considered in this report,

is the probability that a mix and/or a pavement structure will provide satisfactory performance

for a specific design period. To achieve a given level of reliability requires estimates of the

variance in: 1) traffic estimates; 2) variability as a function of asphalt content, degree of

compaction (as measured by air-void content), and aggregate gradation; and 3) pavement

structure variables including asphalt concrete thickness and stiffnesses and thicknesses of the

supporting layers.

This appendix contains a brief summary of both reliability and variability considerations

used to estimate the pay factors presented in this report.

Reliability

As stated above, reliability, as considered herein, is the probability that an asphalt mix or

pavement structure will provide satisfactory performance throughout the selected design period.

The reliability level for each specific situation is set by the designer. Larger levels of reliability

reduce the chances of accepting deficient mixes; however, the tradeoff is the potentially larger

cost associated with reducing the number of acceptable materials or mixes or increasing the

thickness of the asphalt concrete.

Reliability is introduced in the mix design and analysis system by a reliability multiplier,

M, which is calculated as follows:

( ) ( )ESALsNZeM lnvarlnvar += (A-1)

70

in which e = the base of natural or Naperian logarithms, Z = a factor depending solely on the

design reliability, var(ln N) = the variance of the logarithm of the laboratory fatigue or rutting

life under the standard 40-kN (9,000-lb.) wheel load, and var(ln ESALs) = the variance of the

estimate of the logarithm of the deign ESALs. Z is related to design reliability as follows:

Design reliability (percent) Z9590806050

1.641.280.840.2530.000

To estimate the var(ln N) and var(ln ESALs) requires estimates of the variabilities in the

parameters which are used to determine the two variances. These variances are discussed in the

next section.

Variability

Variability associated with forecasts of design ESALs is not well defined at this time.6 In

the absence of better information, var (ln ESALs) has been assumed to 0.300. This estimate is

based primarily on judgement of the authors of this report. As a point of reference, the 1993

AASHTO Design Guide (13) suggests that actual traffic may be 1.6 times that predicted at one-

standard-deviation level. For an assumed log normal distribution, this produces a var(ln ESALs)

of about 0.22. Thus the value selected would appear to be “reasonably” conservative.

The var(ln N), as developed in this analysis, is a function of both testing and construction

variabilities. Two components of construction variability have been considered: those affecting

mix behavior and those affecting permanent structure behavior.

6 Results of the Long Term Pavement Performance (LTPP) Program (12) should eventually provide a better definedestimate of traffic variability.

71

As currently developed, var(ln N) is thus the sum of three components as follows:

( ) 222lnvar smt sssN ++= (A-2)

in which 2ts = the testing variance, 2

ms = the mix variance, and 2ss = the structure variance.

Consider first the testing variance, 2ts , for fatigue. Testing variability reflects a

combination of factors including: 1) the inherent variability in fatigue measurements (associated

both with specimen preparation as well as testing equipment and procedures; 2) the nature of the

laboratory testing program; and 3) the extent of extrapolation necessary for estimating fatigue

life (using a least-squares, best-fit line) at the design strain level. The var(ln N) is calculated as

follows:

( ) ( )( )

�

��

�

�

� −

−++= 2

22 11lnvar

xxq

xXn

sNp

(A-3)

in which s2 = the variance in logarithm of fatigue life measurements, n = the number of test

specimens, X = ln(in-situ strain) at which ln(N) must be predicted, x = average ln(test strain), q

= number of replicate specimens at each test strain level, and xp = ln(strain) at the pth test strain

level.

The mix fatigue study conducted as an initial art of the CAL/APT Program (5) was used

to determine the testing variance. Replication which was built into the experiment design

permitted computation of the inherent variance (s2) in the logarithm of fatigue life measurements.

The experiment design involved 15 different mixes (five asphalt contents and three air-void

contents) tested at each of two strain levels with nominally three replicates at each of the 30

combinations (a few small-strain tests had four replicates). A total of 96 observations were

included in calculating the sample variance using the following relationships:

72

dn

WSSs

d

kk

−= =12 (A-4)

and

( )−==

kn

ikik NNWSS

1

2lnln (A-5)

in which WSSk = within sum of squares for factor level combination k (air-void content, asphalt

content, and strain level), n = number of observations (96), d = number of factor level

combinations (30), lnNi = logarithm of measured fatigue life for specimen i, lnNk = average

logarithm of measured fatigue lives of specimens for factor level k, and nk = number of replicates

at factor level k.

The best estimate of the overall sample variance of the natural logarithm of the fatigue

life was calculated using the aforedescribed procedure to be 0.220. The sample variance

obtained in the SHRP A-003A expanded test program, using the same testing equipment and

procedures, was 0.152. Because of greater replication in the current study [three versus two in

Reference (14)] and smaller strain levels [150 and 300 microstrain versus 400 and 700

microstrain in Reference (14)], 0.220 seems to be the best possible estimate of s2 at the current

time. It was used in developing the shift factors in the mix design and analysis model and is

recommended for use for mix design purposes.

For fatigue, the materials and construction components of variability were determined in

the following manner.

Potentially important mix variables include asphalt content and air-void content.

Fortunately, the necessary data for quantitative evaluation of these variables is available, namely,

construction variances and, for a typical mix, relationships with mix stiffness and fatigue life (5).

Other potentially important mix variables, such as aggregate gradation, were excluded from

73

consideration. This decision was supported by laboratory test data repeated by other

investigators, [e.g., Hicks et al. (15)] and by analyses of the fatigue performance, both in the

laboratory and the field, of the mixes used at WesTrack (2).

Structural variables include thickness of the asphalt concrete layer and stiffnesses and

thicknesses of other supporting layers. Asphalt concrete thickness was a critical factor to be

considered, and construction variance data was available. The supporting layers are more

problematic because knowledge of the variabilities of foundation layer thicknesses and moduli

appears to be limited, and complexity of the necessary analysis increases with increases in the

number of layers. As a result, it was decided to simplify the process by identifying an equivalent

single layer for which effects were similar to the multilayer supporting layers. The equivalent

single layer has been characterized by its modulus, and the variance of this equivalent modulus

was evaluated from post-construction falling weight deflectometer (FWD) measurements.(7)7

Estimates of the variances of asphalt content, air-void content, and asphalt-concrete

thickness were obtained from a combination of literature review and WesTrack test data.

Summary results are presented in Section 3. These totals include not only materials and

construction components but also components resulting from testing and sampling. The latter

components must be removed from the variance estimates in order to isolate materials and

construction effects: Table 3.2, Section 3, summarizes the necessary data.

Table 3.3, Section 3, provides a summary of the quantities used to represent reasonable

estimates of materials/construction variability associated with conventional construction practice.

The equations for estimating the standard deviation of asphalt-concrete thickness were developed

as an approximate way to handle multilift construction. Among the assumptions made in their

7 Table 3.1 in Section 3 contains a listing of the sources of FWD measurements used.

74

development was that the coefficient of variation of thickness in single-lift construction is about

14 percent, as stated in Section 3.

While the testing variance, 2ts can be obtained from direct computations, using Equation

4.3, computing the mix variance, 2ms , and the structure variance, 2

ss , is more complex.

Fortunately, Monte Carlo simulation is a convenient and relatively quick way to obtain the

necessary estimates. For the design pavement structure and test temperature, each simulation

proceeds as follows. A random selection is made of asphalt content and air-void content. The

mix stiffness is determined from these random selections, and a “mean” pavement strain is

calculated (ELSYM5). A randomly selected adjustment is made to this strain level to account

for random variations in surface thickness and support modulus. The fatigue life is then

computed from the random selections of tensile strain and the asphalt and air-void contents. The

process is repeated until the desired degree of convergence has been reached. In work to date,

distributions of all of the four construction variables have been assumed to be normal. The

Monte Carlo simulations include both testing variability and construction variability.

With the variance estimates, Monte Carlo simulation was used to produce estimates of

var(ln N) for the 18 hypothetical pavements summarized in Table B-1 to illustrate the process.

Stiffness and fatigue relationships contained in Section 3 (Equations 3.1 and 3.2) together with

target asphalt and air-void contents of 5 and 8 percent respectively, were utilized.

Figure A-1 illustrates the level and components of var(lnN) for each of the 18 structures.

The testing portion of the total variance increases significantly with the increases in pavement

thickness associated with larger traffic indices principally because of the increased level of

extrapolation to the smaller strain levels. Construction variability is important for all of the

pavements but is a much greater portion of the total variability for the less substantial pavements

75

which accompany smaller traffic indices. The structures component of construction variability is

slightly greater for thinner than for thicker pavements while a reverse trend is observed for the

mix component.

0

0.5

1

1.5

2

2.5

7CTB

5

7CTB

20

7CTB

40

7AB5

7AB2

0

7AB4

0

11C

TB5

11C

TB20

11C

TB40

11AB

5

11AB

20

11AB

40

15C

TB5

15C

TB20

15C

TB40

15AB

5

15AB

20

15AB

40

Pavement Section

Varia

nce

of L

n(N

)

Structure

Mix

Test

Figure A-1. Major components of testing and construction variance.

77

78

APPENDIX B

Table B-1 Pavement Structures

Designation Layer TargetThickness (in.)

Modulus(psi)

Poisson’sRatio

Target StandardDeviation

7AB20

SurfaceBaseSubbaseSubgrade

3.67.26.0-

Variable30,00020,00012,200

0.400.450.450.50

0.314

9AB20


6.66.67.8-

Variable30,00020,00012,200

0.400.450.450.50

0.476

11AB20


9.66.08.4-

Variable25,00020,00012,200

0.400.450.450.50

0.620

13AB20


10.27.812.6-

Variable25,00020,00012,200

0.400.450.450.50

.0640

79

APPENDIX C: ANALYTICALLY-BASED APPROACH TO RUTTING PREDICTION

As a part of the WesTrack Project to develop a performance related specification (PRS)

for asphalt concrete (AC) construction, two approaches to develop performance models for

rutting were developed.(2) One, based on regression of both field and laboratory test data, has

been described in Section 3 herein and used to develop pay factors for rutting included in Section

4. The other, though not used, is briefly described in this Appendix so that it might serve to

provide a more general approach to pay factor determination if so desired. It is referred to as a

mechanistic-empirical performance model.

Mechanistic-Empirical Approach

In this approach, the pavement is assumed to behave as a multi-layered elastic system.

An idealization of a specific asphalt pavement is show in Figure C-1 together with key

parameters used to estimate rut depth development with traffic, i.e., τ, γe, and εv.*

The three parameters can be determined on an hour-by-hour basis and a program like the

Integrated Climate Model (ICM) (16) can be used to define temperature distributions both with

time and depth in the AC to permit estimates of mix stiffnesses. For convenience, if a program

like ELSYM5 is used, it is recommended that the AC layer be subdivided into three layers with

thicknesses from top to bottom of 25 mm (1 in.), 50 mm (2 in.), and the remaining AC thickness

as the third layer to simulate the effects of temperature gradients on mix stiffness. In the

computations a constant Poisson’s ratio of 0.35 is suggested. If programs are available with

capability of treating more than 5 layers, the third layer can be further subdivided to produce a

*τ, γe = elastic shear stress and strain at a depth of 50 mm (2 in.) below outside edge of tire εv = elastic vertical compressive strain at the subgrade surface

80

more representative stiffness distribution in the AC layer.

Moduli of the underlying layers can also be varied to reflect seasonal influences on the

stiffness moduli of those layers. Poisson’s ratio in the range 0.35 to 0.4 are recommended for

untreated granular layers and 0.4 to 0.45 for untreated fine-grained (subgrade) soils.

In this approach, rutting in the asphalt concrete was assumed to be controlled by shear

deformations. Accordingly, the computed values for τ and γe at a depth of 50 mm (2 in.) beneath

the edge of the tire are used for the rutting estimates, as shown in Figure C-1. Densification of

the asphalt concrete is excluded in these estimates since it has a comparatively small influence

on surface rutting.

In simple loading, permanent shear strain in the AC is assumed to accumulate according

to the following expression:

( ) cei nba γτγ exp⋅= (C-1)

where

iγ = permanent (inelastic) shear strain at 50 mm (2 in.) depth

τ = shear stress determined at this depth using elastic analysis

eγ = corresponding elastic shear strain

n = number of axle load repetitions

a, b, c = regression coefficients

81

50 mm (2 in.)

τ, γe

Asphalt ConcreteEAC, νAC

BaseEbase, νbase

∞

SubgradeEsub, νsub

εv

300 mm (12 in.)

150 mm (6 in.)

Figure C-1. WesTrack pavement respresentation for mechanistic-empirical modeling forrutting.

The time-hardening principle is used to estimate the accumulation of inelastic strains in

the asphalt concrete under in-situ conditions. The resulting equations are as follows:

( ) ejj baa γτexp⋅= (C-2)

[ ]ci na 111 ∆=γ (C-3)

( )( ) ccj

ij

ij naa �

�� ∆+= − 1

11γγ (C-4)

where:

j = jth hour of trafficking

γ = elastic shear strain at the jth hour

82

∆n = number of axle load repetitions applied during the jth hour

The concept is illustrated schematically in Figure C-2.

Rutting in the AC layer due to the shear deformation is determined from the following:

ijAC Krd γ= (C-5)

K ranges from about 5.5 for a 150-mm (6-in.) layer to 10 for a 12-in. thick AC layer when the rut

depth, rdAC, is expressed in inches.(17)

To estimate the contribution to rutting from base and subgrade deformations, a

modification to the Asphalt Institute subgrade strain criteria (18) is utilized. The equation

expressing the criterion for 12.5 mm (0.5 in.) of surface rutting is:

484.491005.1 −−×= vN ε (C-6)

where:

N = the allowable number of repetitions

εv = the compressive strain at the top of the subgrade

Since these criteria do not address rutting accumulation in the pavement structure, rut

depth (rd) contributed by the unbound layers was assumed to accumulate as follows:

ednrd = (C-7)

where

d, e = experimentally determined coefficients

ln number of load applications

ln in

elas

tic s

trai

n

1st load block

2nd load block

3rd load block

4th load block5th load block

6th load block

7th load block

8th load block

9th loadblock

10th load block

Inelastic strain-nrelationship for

smaller load

Inelastic strain-nrelationship for

larger load

Figure C-2. Time-hardening provedure for plastic strain accumulation under stress repetitions of different magnitudes incompound loading.

83

84

Least squares analyses for the WesTrack data suggest that the value for d in Equation C-7

using the Asphalt Institute criteria is:

[ ]evfd 484/491005.1 −−×= ε (C-8)

where:

f = 3.548

e = 0.372

Using the time-hardening principle, as was used for the asphalt concrete, rut depth

accumulation can be expressed in a form similar to Equation (C-4), i.e.:

( )[ ] 372.0372.011 jjjjj ndrddrd ∆+= − (C-9)

The framework for rut-depth estimation, using Equations C-1, C-4, and C-9 is illustrated

in Figure C-3. This approach has a distinct advantage over the direct regression approach in that

it permits prediction of rut depth as a function of traffic and environment as well as a function of

mix parameters.

For WesTrack, 13 sections were used to calibrate the coefficients of Equations C-1 and

C-7. Initially, a value for b = 0.0487 in Equation C-1 was used based on the results of RSST-CH

tests. Subsequently, a value of b = 0.071 (10.28 in metric units) was determined to provide

better correspondence between measured and computed rut depths.

Using the procedure illustrated in Figure C-3, least squares regression provided values of

a and c for each of the 23 WesTrack sections where rutting without observed fatigue cracking

was obtained. These are summarized in Table C-1. It will be noted that the average root mean

square error (RMSE) for rut depth for the 24 sections is 0.051 in. Figures C-4, C-5, C-6, and C-7

illustrate comparisons between computed and measured rut depths for Section 4 (fine), Section

19 (fine-plus), Section 7 (coarse), and Section 38 (replacement, coarse).

85

Begin

Select day and hour

Determine pavementtemperature distribution

Determine moduli ofelasticity

Compute stresses andstrains at key locations

Accumulate inelasticstrains in asphalt concrete

Estimate rut depth in alllayers

End

More iterations?

Figure C-3. Framework for rut depth estimates.

Table C-1 Calculated ESALs to a range in rut depths for a constant loading of 60 trucks/hour, WesTrack environment.ESALs to rut depth, in.

Section 2.5 mm 5.1 mm 7.6 mm 10.2 mm 12.7 mm 15.2 mm 17.8 mm Vair PWasp P200

1 28,039 252,287 820,069 3,591,871 9,204,604 18,398,845 8.6 5.69 5.14 236,708 611,416 1,359,344 2,773,927 3,863,423 5,878,847 7,019,202 6.9 5.24 4.47 63,999 153,055 227,630 316,256 408,645 513,061 624,134 7.6 6.28 6.49 110,563 234,749 352,391 497,064 651,076 854,130 1,082,798 3.2 6.07 5.211 117,174 482,548 2,448,516 6,534,875 12,923,017 8 5.5 5.512 116,657 435,335 1,585,887 5,124,824 9,010,004 15,295,397 3.8 5.35 613 95,473 225,983 355,542 517,591 707,157 945,578 1,273,364 6 6.01 5.714 10,769 161,277 329,455 962,944 3,077,647 6,489,484 11,865,398 7.7 6.22 4.915 29,167 287,582 1,834,871 6,728,613 16,439,353 8.8 5.55 5.218 189,538 666,122 2,747,063 6,158,581 9,973,563 15,910,029 4.6 6.22 5.119 18,607 180,272 368,802 1,021,007 2,988,579 5,954,150 9,437,925 6 5.41 5.820 8,338 92,423 234,398 499,951 1,380,435 3,205,796 6,357,843 10.4 5.4 5.221 76,781 176,680 255,239 346,170 455,231 556,356 688,619 3.6 6.25 5.422 7,119 177,636 916,839 8,948,966 6.9 4.76 5.323 69,331 224,904 446,813 905,331 2,231,318 3,215,667 5,376,272 5.8 5.78 724 26,867 105,733 202,299 308,313 447,466 632,476 929,569 7.5 5.9 6.625 58,393 153,644 234,776 335,143 459,322 584,865 766,798 3.1 6.33 6.735 929 3,339 53,879 375,289 2,160,805 3,499,640 8.75 6.12 5.637 2,971 23,206 85,712 217,934 461,473 1,216,154 9.55 6.14 5.738 819 31,835 489,242 3,054,882 7,271,094 16,890,972 7.7 5.55 6.239 1,530 47,133 489,200 2,725,955 5,423,810 10,857,714 5.5 5.94 5.754 902 2,835 44,886 276,540 1,991,198 3,010,916 7.3 6.11 5.855 2,282 29,129 89,868 231,453 454,256 883,673 1,985,619 4.3 6.04 6

(1 in. = 25.4 mm)

86

0

2

4

6

8

10

12

14

16

18

10/28/1995 2/5/1996 5/15/1996 8/23/1996 12/1/1996 3/11/1997 6/19/1997 9/27/1997 1/5/1998 4/15/1998 7/24/1998 11/1/1998

Year

Max

imum

rut d

epth

, mm

Total rut - baseTotal predicted rutTotal measured rut

Figure C-4. Comparison between computed and measured rut depth versus time; Section 4.

87

0

3

6

9

12

15

18

21

24

27

30

2/5/1996 3/26/1996 5/15/1996 7/4/1996 8/23/1996 10/12/1996 12/1/1996

Year

Max

imum

rut d

epth

, mm


(1 in. = 25.4 mm)Figure C-5. Comparison between computed and measured rut depth versus time; Section 7.

88

0

3

6

9

12

15

18

10/28/1995 2/5/1996 5/15/1996 8/23/1996 12/1/1996 3/11/1997 6/19/1997 9/27/1997 1/5/1998 4/15/1998 7/24/1998 11/1/1998

Year

Max

imum

rut d

epth

, mm



89

0

3

6

9

12

15

18

6/19/1997 9/27/1997 1/5/1998 4/15/1998 7/24/1998 11/1/1998 2/9/1999 5/20/1999

Year

Max

imum

rut d

epth

, mm



90

91

Expressions reported in Reference (2) for defining field a and c could be used if mixes

similar to those used at WesTrack are being evaluated. For wider applications, however, it is

desirable to have relationships not limited to these types of mixes.

An approach recommended at this time makes use of the results of the laboratory RSST-

CH test and the mix variables-asphalt content and air-void content-to determine field a and c

values. A series of regressions were performed for the 23 WesTrack sections shown in Table C-

1 considering these variables. Results of the calibrations are shown in Table C-2 for ln(field a)

and Table C-3 for field c. In these tables, lab a is from the expression:

bi an=γ (C-10)

obtained from analysis of the RSST-CH results as shown in Figure C-8. The term rsst 5

corresponds to the repetitions corresponding to a value of γi = 5 percent, also illustrated in Figure

C-8.

From the analyses, Regression 6 in both Tables C-2 and C-3 is recommended for use to

define a and c for use in the ME procedure briefly summarized herein.

Table C-2 Calibration of equations for simulating ln(field a) based on mix and RSSTvariables.

Regr. 1 Regr. 2 Regr. 3 Regr. 4 Regr. 5 Regr. 6Constant 14.9116 24.7107 24.3317 24.9718 25.3649 20.4844PWasp -3.67001 -5.02990 -5.04342 -5.23716 -5.71438 -5.12624Vair 0.313875PWasp·Vair 0.0823738rsst5 6.219E-05 9.699E-05laba 1301.81 1622.41 1745.07 1858.91 2472.96 2264.05R2 0.611 0.629 0.684 0.752 0.888 0.951SectionsOmitted None 14 14, 15 1, 14, 15 1, 14, 15,

191, 4, 14, 15,

19

92

0.0001

0.001

0.01

0.1

1 10 100 1000 10000 100000RSST Repetitions

Perm

anen

t She

ar S

train

3778

5 %

Figure C-8. Permanent shear strain, iγ , versus load repetitions, n; rsst = 3778.

92

93

Table C-3 Calibration of equations for simulating field c based on mix and RSSTvariables.

Regr. 1 Regr. 2 Regr. 3 Regr. 4 Regr. 5 Regr. 6Constant -0.944102 -1.75309 -1.72144 -1.77798 -1.83917 -1.49931PWasp 0.312598 0.426673 0.427803 0.444915 0.493348 0.452398Vair -0.0217923PWasp·Vair -0.0064968rsst5 -6.216E-06 -8.575E-06lab a -87.5258 -113.452 -123.693 -133.748 -190.11 -175.759R2 0.556 0.591 0.648 0.728 0.890 0.936SectionsOmitted None 14 14, 15 1, 14, 15 1, 14, 15,

191, 4, 14, 15,

19

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